There is 32 students in class.8 boys out of 20 wear cap and 8 girls out of 12 wear spectacles find the probability that the student is boy who wears cap or girls who doesn't wear spectacles ​

Answer:

Integral

Step-by-step explanation:

explain integral calculus

The slope of this linear function is equal to: B. -2/9.

The volume of a cylinder with a height of 10 m and a radius of 5 m is equal to 785 m³.

The value of each expression is: C. a) 2, b) 1/2, c) 2/9.

In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (8 - 10)/(6 - (-3))

Slope (m) = (8 - 10)/(6 + 3)

Slope (m) =

Slope (m) = -2/9.

In Mathematics, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given parameters, we have:

Volume of cylinder, V = 3.14 × 5² × 10

Volume of cylinder, V = 785 m³

(√2)² = 2

(1/√2)² = 1/2

(√2/3)² = 2/9

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The sine function with the desired features is given as follows:

F(x) = sin(3.5π(x + π/2)) + 1.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are listed as follows:

The function has an amplitude of 1, hence the parameter A is given as follows:

A = 1.

The period is of 4/7, hence the coefficient B is given as follows:

2π/B = 4/7

4B = 14π

B = 3.5π.

The function contains the point (-π, 2), hence the phase shift and the vertical shift are given as follows:

Hence the function is:

F(x) = sin(3.5π(x + π/2)) + 1.

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Answer:

What is the Value of Tan 270 Degrees? The value of tan 270 degrees is undefined. Tan 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .) ⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .

please marke a a brainalist pls

FALSE. Every random sample of the same size from a given population will not produce exactly the same confidence interval for μ.

The confidence interval is a statistical measure used to estimate the range of values within which a population parameter is likely to fall. The confidence interval is calculated based on the sample mean and standard deviation, as well as the level of confidence desired.

Suppose we take a random sample of size n from a population, and calculate the confidence interval for the population mean using this sample. The sample mean and the sample standard deviation will be used to estimate the true population mean and the population standard deviation, respectively. However, as the sample is random, each sample—despite being drawn from the same population—will have different values for the sample mean and standard deviation. Thus, different samples will produce different confidence intervals for the population mean.

Moreover, the size of the sample also affects the width of the confidence interval; larger samples tend to produce more precise estimates of the population mean, while smaller samples yield larger confidence intervals. Therefore, random samples of different sizes from a given population will also produce different confidence intervals.

In summary, the confidence interval is a statistical measure that provides a range of likely values for the population parameter, such as the population mean. While it can be calculated using any random sample from a population, different samples of the same size or different sizes will generally produce different confidence intervals.

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The intersection of two parallel lines; x = 10 metres.

Alternate angles are created when two parallel lines are intersected by a transversal. Have a look at the given illustration; the two parallel lines are EF and GH. When a transversal splits two parallel lines, the alternate angles are equal.

The alternate interior angles are equal because of the parallel lines characteristic.

Angle STQ (denoted as 2x+10) and angle RQS are hence equal. Angle QRP (shown as x+20) and angle RQS are likewise equal.

Setting these two angles equal to each other, we can get:

x+20 = 2x+10

Simplifying this equation, we get:

x = 10.

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The answers are a)the sample mean, which is $1,235. b) margin of error = $58.50. c)95% .d)the average monthly rent is at least $1,300.e)The z-score for a 92% confidence interval is 1.75.

a) The sample mean is the point estimate of the true mean monthly rent for one-bedroom apartments available for rent near BCIT, which is $1,235.

(b) At a 95% confidence level, the margin of error on the true mean monthly rent estimate is calculated as follows:

Margin of error = Z * (standard deviation / square root of sample size), where Z is the desired confidence level's z-score, which is 1.96 for a 95% confidence level.

Thus, the margin of error is equal to 1.96 * (150 / sqrt(36)) = $58.50.

(c) The 95% confidence interval for the true mean monthly rent is calculated as follows:

Lower value = point estimate minus margin of error = $1,235 minus $58.50 equals $1,176.50

Upper estimate + margin of error = $1,235 + $58.50 = $1,293.50.

(d) To see if the confidence interval supports the friend's claim that the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300, we need to see if the lower limit of the confidence interval is greater than or equal to $1,300.

Given that the confidence interval is $1,176.50 $1,300, we can conclude that the confidence interval does not support the friend's claim that the

average monthly rent is at least $1,300. As a result, the answer is "No."

(e) A standard normal distribution table or calculator can be used to calculate the z-score corresponding to a 92% confidence interval.

A 92% confidence interval has a z-score of 1.75. (to two decimal places).

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Answer:

Step-by-step explanation:

Since they are traveling in the same direction, the distance between them increases at a rate of the difference of their speeds.

The relative speed of train A with respect to train B is:

105 kmph - 87 kmph = 18 kmph

In three hours, the distance between them will be:

Distance = Speed x Time

Distance = 18 kmph x 3 hours

Distance = 54 km

Therefore, the two trains will be 54 kilometers apart after three hours.

The graph's function limit at x=4 is 6.

In mathematics, the limit of a function is the value that the function approaches as the input approaches a certain value or as the input approaches infinity or negative infinity. A function may or may not have a limit at a given point or as the input goes to infinity or negative infinity.

The formal definition of the limit of a function f(x) as x approaches a value a is as follows:

For every positive number ε (epsilon), there exists a corresponding positive number δ (delta) such that if 0 < |x-a| < δ, then |f(x)-L| < ε.

Limit f(x) at x tend to 4⁺ =6.

Limit f(x) at x tend to 4⁻ =6

Hence, the graph's function limit at x=4 is 6.

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Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).

By determining the value of a single unit or quantity and then scaling that value up or down to determine the value of another quantity, the unitary method is a mathematical strategy used to solve problems. According to the unitary method's guiding concept, if one quantity or unit has a certain value, then a predetermined number of those same quantities or units will have a proportionate value. For instance, 5 apples would cost $5 if 1 fruit cost $1.

given

We can use the person's weight and body fat proportion to determine how many pounds of body fat they have. We can commence by calculating the decimal weight of the body fat:

weight of body fat Equals body fat percentage * weight

= 0.163% * 163 lbs.

= 26.509 lbs.

Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).

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The product of the number 3/4 and 8 1/2 is 51/8.

A mixed number is one that has a fraction and a whole number, separated by a space. An example of a mixed number is 8 1/2. Contrarily, an improper fraction is one in which the numerator exceeds or is equal to the denominator. For instance, 17/2 is a bad fraction. An improper fraction is a fraction in which the numerator is more than or equal to the denominator, as opposed to a mixed number, which combines a whole number with a proper fraction.

The given numbers are 3/4 and 8 1/2.

Convert the mixed number to an improper fraction:

8 1/2 = (8 x 2 + 1) / 2 = 17/2

Then, we can multiply the fractions:

3/4 x 17/2 = (3 x 17) / (4 x 2) = 51/8

Hence, the product of 3/4 and 8 1/2 is 51/8.

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Therefore, the only statement that is true is: "The new area is 6 times the original area."

Area is a measure of the size or extent of a two-dimensional surface or region, such as the surface of a square, rectangle, circle, triangle, or any other shape. It is expressed in square units, such as square meters, square feet, or square centimeters.

Here,

If the side lengths of a square are tripled, the new side length will be 2 mm x 3 = 6 mm.

The original area of the square is:

Area = side length x side length = 2 mm x 2 mm = 4 mm²

The new area of the square with tripled side lengths will be:

New area = new side length x new side length = 6 mm x 6 mm = 36 mm²

Therefore, the new area of the square will be 36 mm².

To determine which of the following statements about its area will be true, we need to see which statements are true for the new area of 36 mm²:

A. The new area is 6 times the original area. This statement is true because 36 mm² is 6 times larger than 4 mm².

B. The new area is 3 times the original area. This statement is false because 36 mm² is 9 times larger than 4 mm², not 3 times larger.

C. The new area is equal to the original area. This statement is false because the new area of 36 mm² is much larger than the original area of 4 mm².

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Complete question:

look at this square: 2 mm 2 mm if the side lengths are tripled, then which of the following statements about its area will be true?

The ratio of the new area to the old area will be 2:1

The ratio of the new area to the old area will be 6:1.

The ratio of the new area to the old area will be 1:2.

The ratio of the new area to the old area will be 4:1.

Answer:

D

Step-by-step explanation:

7/1 times 3/4 equals 21/4 cups of milk

The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.

To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.

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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.

138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.

Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.

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The width of the top of the bookcase should be approximately 12.2 inches to give Bria's soap carving collection an area of 300 square inches.

Simply multiply the length and width measurements to get the area of your square or rectangular area in square inches.

Assume the bookcase's top is rectangular, with length "L" and width "b". Because the area of a rectangle is the product of its length and width, we get:

L * b = 300

To find "b," we can rearrange the equation as follows:

b = 300 / L

We don't have enough information to directly solve for "L," but we can make an educated guess based on the figure provided. Based on the illustration, the bookcase appears to be roughly twice as long as it is wide. So let us suppose:

L ≈ 2b

When we plug this into the equation above, we get:

b = 300 / (2b) (2b)

To simplify, we have:

b^2 = 150

When we take the square root of both sides, we get:

b ≈ 12.2

We have, rounded to the nearest tenth of an inch:

b ≈ 12.2 inches

As a result, the width of the top of the bookcase should be approximately 12.2 inches in order to give Bria's soap carving collection a 300-square-inch area.

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Answer:y=x-5

Step-by-step explanation:this is the answer for sure

Answer:

[tex]y=x-5[/tex]

Step-by-step explanation:

Notice for every X you do increase your Y by 1, this is the slope must be 1, to check you can use the slope equation with any two points

[tex]m= \frac{-4-(-3)}{1-(2)} =-1[/tex]
The lets use one point and the line equation:

[tex]y-yo=m(x-xo)[/tex]
[tex]y+4=-1(x-1)[/tex]

Solving for Y you can obtain

[tex]y=x-5[/tex]

You can input any X value and check the Y value to be sure, for example, for X=3 you can check Y=3-5=-2. In the table for X=3 the Y value is -2, so this checks.

The description of the ensembles would be: 1. Students who attend both recitals, 2. Students who attend one of the two recitals, 3. students who attend both recitals, 4.The difference between the set P and U, that is, 3 students.

To graph the information in a Venn diagram we must take into account the information in the statement. In this case we must place 6 students outside the circles because there are 6 who do not attend any activity.

So, there would be 34 remaining students, of which 20 go to the piano recital and 23 to the voice recital. So, we can establish that 20 go to both recitals, 3 go to the voice recital, and 1 go to the piano recital.

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After labeling with the corresponding boxes , The statements which describes Red pulp and white pulp are as follow:

1. Red pulp           2. Red Pulp        3. White Pulp        4. Red pulp    

5. White Pulp        6. White Pulp        7. Red Pulp.

Red Pulp:

The red pulp of the spleen is made up of connective tissue (also known as Bill Roth's cord) and numerous sinusoids of the spleen which appear red due to excess blood. Its main function is to filter antigens, microorganisms and defective or worn out red blood cells from the blood.

The spleen consists of red and white pulp, separated by the marginal zone; 76-79% of a normal spleen is made up of red pulp. Unlike white pulp, which contains mostly lymphocytes (such as T cells), red pulp is made up of several types of blood cells, including platelets, granulocytes, red blood cells, and plasma.

White Pulp:

White pulp is the histological name for the areas of the spleen (so called because they appear whiter in rough sections than the surrounding red pulp), which make up approximately 25% of the spleen. The white pulp is entirely composed of lymphoid tissue.

Specifically, the white pulp contains several regions with distinct functions:

The periarteriolar lymphatic sheaths (PALS) are usually associated with the arteriolar supply to the spleen; they contain T lymphocytes.

Lymphoid follicles with dividing B lymphocytes located between the PALS and the marginal zone bordering the red pulp. This region produces IgM and IgG2.

These molecules play a role in the opsonization of extracellular organisms, in particular encapsulated bacteria.

The marginal zone exists between the white pulp and the red pulp. It is located away from the central arterioles, close to the red pulp. It contains antigen-presenting cells (APCs), such as dendritic cells and macrophages. Some white pulp macrophages are of a special type called metallolipid macrophages.

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The answer of the given question based on finding the missing length of a triangle the answer is , None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.

In geometry,  triangle is  two-dimensional polygon with three straight sides and three angles. It is one of  basic shapes in geometry and can be defined as  closed figure with three line segments as its sides, where each side is connected to two endpoints called vertices. The sum of  interior angles of  triangle are 180° degrees.

Triangles are classified based on length of their sides and  measure of their angles. A triangle can be equilateral, isosceles, or scalene based on whether all sides are equal, two sides are equal, or all sides are different, respectively.

To find the missing length indicated, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

In this triangle, we can see that the two legs have lengths of 9 and 16, and the hypotenuse has length X. So we can write:

9²+ 16² = X²

Simplifying the left-hand side:

81 + 256 = X²

337 = X²

Taking the square root of both sides (and remembering that X must be positive, since it is a length):

X = sqrt(337)

X ≈ 18.3575

So the missing length indicated is approximately 18.3575. None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.

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The standard normal area is the region under the standard normal distribution curve, which has a mean of 0 and a standard deviation of 1. One is equal to the entire area under the normal distribution curve.

To determine the probability for the above intervals using a typical normal distribution table or a calculator with a normal distribution function:

[tex]P(1.22 < Z < 2.15) = 0.1143[/tex]

[tex]P(2.00 < Z < 3.00) = 0.0228[/tex]

[tex]P(-2.00 < Z < 2.00) = P(Z < 2.00) - P(Z < -2.00) = 0.9772 - 0.0228 = 0.9544[/tex]

The number of standard deviations the variable is from the mean is shown by the ensuing Z-score. The chance of detecting a certain value of the variable in a given interval can then be determined using the standard normal area.

Therefore, The symmetry of the normal distribution allows us to use the third interval's coverage of 4 standard deviations to simplify the calculation, as illustrated above.

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As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.

given

AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.

We can apply the Pythagorean theorem to segment AB as follows:

[tex]AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2[/tex]

AB² = 50

AB = √50 = 5√2

As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

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The resultant force is equal to F1, which is {-300i + 170j + 190k}N, and the couple moment acting at point 0 is  (-0.19i - 0.34j + 0.15k) N.m.

To determine the resultant force acting at point O, we can add all the forces acting at point O. In this case, we have only one force F1 = {-300i + 170j + 190k}N. Therefore, the resultant force acting at point O is F1 itself.

To determine the couple moment acting at point O, we can use the formula:

M = r x F

where r is the position vector from point O to any point on the line of action of force F.

Since we don’t know the position vector r, we can choose any arbitrary point on the line of action of force F. Let’s say we choose point A which lies on the line of action of force F and is perpendicular to it.

Therefore, r = OA where OA is the position vector from point O to point A. We can find OA by subtracting position vectors of points O and A i.e., OA = A - O.

Now, let’s calculate M using M = r x F.

M = (OA) x F1

M = (A - O) x {-300i + 170j + 190k}N M

= (-0.19i - 0.34j + 0.15k) N.m

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Complete question is:

Replace the loading system by an equivalent resultant force and couple moment acting at point o. Assume F1 = {-300i + 170j + 190k}N

Part A Determine the resultant force. Enter the 2, y and a components of the resultant force separated by commas.

Part B Determine the couple moment acting at point 0. Enter the x, y and 2 components of the couple moment separated by commas.

The vertex is frequently identified by the letter that appears in the middle, like the letter V. Angles are often measured in degrees, and degrees are used to characterize angles. Thus, option C is correct.

Angle 7 is perpendicular to angle 3, and angle 3 is supplementary to angle 8, therefore they both fall along a straight line. Hence, angle 8 is complementary to angle 7.

Since they form a straight line and are opposite angles, angles 5 and 7 are supplementary. Hence, angle 5 is complementary to angle 7.

The only angle in the figure that is not a support for angle 7 is angle 6. If angles 6 and 7 do not overlap but share a vertex and side, then they are considered neighbouring.

Because they do not go to a straight line, angles 6 and 7 are not extra in this case. The answer is therefore Angle 6.

Therefore, They are not always complementary, even if two nearby angles come together to create a straight line.

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The appropriate 0.5 adjusted formula for normal approximation is option (d) p(x > 8.5)

The appropriate 0.5 adjusted formula for normal approximation to approximate binomial probabilities when n is large is

P(Z > (x + 0.5 - np) / sqrt(np(1-p)))

where Z is the standard normal variable, x is the number of successes, n is the number of trials, and p is the probability of success in each trial.

To approximate binomial probability p(x > 8) when n is large, we need to use the continuity correction and find the appropriate 0.5 adjusted formula for normal approximation. Here, x = 8, n is large, and p is unknown. We first need to find the value of p.

Assuming a binomial distribution, the mean is np and the variance is np(1-p). Since n is large, we can use the following approximation

np = mean = 8, and

np(1-p) = variance = npq

8q = npq

q = 0.875

p = 1 - q = 0.125

Now, using the continuity correction, we adjust the inequality to p(x > 8) = p(x > 8.5 - 0.5)

P(Z > (8.5 - 0.5 - 8∙0.125) / sqrt(8∙0.125∙0.875))

= P(Z > 0.5 / 0.666)

= P(Z > 0.75)

Therefore, the correct option is (d) p(x > 8.5)

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The given question is incomplete, the complete question is:

To approximate binomial probability p(x > 8) when n is large, identify the appropriate 0.5 adjusted formula for normal approximation. a) p(x > 7.5) b)  p(x >= 9) c) p(x > 9) d) p(x > 8.5)

Answer:

The correct answer is (b+2)

Step-by-step explanation:

(3b-7) + (-2b+9)

3b-7-2b+9

3b-2b+9-7

b+2 Ans

Answer:

b+2 is the answer of this expression.

Step-by-step explanation:

(3b-7) and (-2b+9)

3b+(-2b) + (-7+9)

(3b-2b) + 2

b+2

Answer:

So the lengths of the legs are approximately 8.6 cm and 15.6 cm.

Step-by-step explanation:

Let's call the smaller leg "x" and the larger leg "x + 7". According to the Pythagorean theorem, we know that:

x^2 + (x + 7)^2 = 17^2

Expanding the square on the left side and simplifying, we get:

2x^2 + 14x - 210 = 0

Dividing both sides by 2, we get:

x^2 + 7x - 105 = 0

Now we can solve for x using the quadratic formula:

x = (-7 ± sqrt(7^2 - 4(1)(-105))) / 2(1)

x = (-7 ± sqrt(649)) / 2

x ≈ -15.6 or x ≈ 8.6

Since we're dealing with lengths of sides in a triangle, we can't have a negative value for x. So we discard the negative solution and conclude that the smaller leg is approximately 8.6 cm.

To find the larger leg, we add 7 to x:

x + 7 ≈ 15.6 cm

Answer:

(15+x)÷4 = 80-x

by criss cross we'll get:

15+x = 4(80-x)

15+x = 320-4x

x+4x=320-15

5x = 305

x = 61

For a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.

L'Hospital's rule applies to limit expressions of the form 0/0 or infinity/infinity. Specifically, if we have a limit expression of form f(x)/g(x), where f(x) and g(x) both approach 0 or infinity as x approaches a certain value, then L'Hospital's rule may be applied to find the limit of the expression.

It is important to note that L'Hospital's rule can only be applied if the limit of the derivative of f(x) divided by the derivative of g(x) exists and is finite, or if the limit of the derivative of f(x) divided by the derivative of g(x) approaches infinity or negative infinity.

Therefore, for a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.

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