when x=1,2,3,.... find limit x->infinity
choice
a. 0
b. 1
c. 2
d. 3
f. 4
help me!!!
Answers
Let y = √x, so the limit can be rewritten as
[tex]\displaystyle \lim_{y\to\infty}\left(\frac{\sqrt{y^6+y^2}}{y^2+3} - \frac{\sqrt{y^4+1}}{y+4}\right)[/tex]
Now,
[tex]\sqrt{y^6+y^2} = \sqrt{y^2\left(y^4+1\right)} = y\sqrt{y^4+1}[/tex]
so we can rewrite the limit further as
[tex]\displaystyle \lim_{y\to\infty}\left(\frac{y}{y^2+3} - \frac1{y+4}\right)\sqrt{y^4+1}[/tex]
Combine the rational terms:
[tex]\dfrac y{y^2+3} - \dfrac1{y+4} = \dfrac{y(y+4)-(y^2+3)}{(y^2+3)(y+4)} = \dfrac{4y-3}{(y^2+3)(y+4)}[/tex]
Then in the limit, we get
[tex]\displaystyle \lim_{y\to\infty}\frac{(4y-3)\sqrt{y^4+1}}{(y^2+3)(y+4)} = \lim_{y\to\infty}\frac{(4y^3-3y^2)\sqrt{1+\dfrac1{y^4}}}{y^3+4y^2+3y+12} \\\\ = \lim_{y\to\infty}\frac{\left(4-\dfrac3y\right)\sqrt{1+\dfrac1{y^4}}}{1+\dfrac4y+\dfrac3{y^2}+\dfrac{12}{y^3}} = \boxed{4}[/tex]
Related Questions
URGENT HELP PLS AND THANK U
Answers
Answer: a= 1
Step-by-step explanation:
a * b = b
Divide by “b” on both sides
a= b/b
“b/b” is equal to 1
a=1
Hope that helps
Lmk if you need a better explanation.
Find the missing probability of 3
Answers
Function f is graphed. According to the graph, is f even, odd, or neither?
Answers
Answer:
C
Step-by-step explanation:
f is neither even nor odd
rachel rides her bicycle due east at 9 miles per hour amos rides his bicycle due north at 12 miles per hour if they left from the same point at the same time how far apart will they be after 1 hour
Answers
The distance between Rachel and Amos after one hour is 15 miles.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Distance travelled by Rachel after one hour = 9 mph * 1 h = 9 miles
Distance travelled by Amos after one hour = 12 mph * 1 h = 12 miles
Let x represent the distance between Rachel and Amos, hence:
x² = 9² + 12²
x = 15
The distance between Rachel and Amos after one hour is 15 miles.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Using the Pythagorean Theorem, they will be 15 miles apart after one hour.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, considering their directions, their distance is the hypotenuse of a right triangle of legs 9 miles and 12 miles, hence:
[tex]d^2 = 9^2 + 12^2[/tex]
[tex]d = \sqrt{9^2 + 12^2}[/tex]
d = 15 miles
More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982
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a colleague needs to move a 500 pound object that's on a lever. the fulcrum is 6 inches from the object. If your colleague weighs 180 pounds how far will your colleague need to be from the fulcrum to move the object? Use the formula B = (P x A) ÷ W, and round your answer to two decimal places.
Answers
Answer:
Step-by-step explanation:
The easier way to figure this is by using the concept of torque in physics. If the torque of the man is greater than that experienced by the box, the lever will tilt in the man's favor (in other words, he will move down and the box will be lifted). Torque is found by multiplying the perpendicular force by the length of the lever arm. Because we want the man's torque to be greater than the box's torque, the inequality is:
[tex]\tau_{man}>\tau_{box}[/tex] and
[tex]180r>500(.1524)[/tex] That decimal is 6 inches in terms of meters.
180r > 76.2 so
r > .42 meters or `16.67 inches. The man has to sit at a distance greater than 16.67 inches in order for the box to be lifted by the lever.
7(8+a)=189 please help and give me step by step
Answers
Answer: a = 19
Step-by-step explanation:
Given
7 (8 + a) = 189
Divide 7 on both sides
7 (8 + a) / 7 = 189 / 7
8 + a = 27
Subtract 8 on both sides
8 + a - 8 = 27 - 8
a = 19
Hope this helps!! :)
Please let me know if you have any questions
56 + 7a = 189
7a = 133
a = 19
Geometry - Triangle d) In the given figure, BE = EC and CE is the bisector of ZACB. Prove that ZBEC = ZACD. E B D С
Answers
Answer:
Let m∠BCE = x
Then m∠ACE = x as well since CE is bisecting ∠ACB.
m∠ACD + x + x = 180° ⇒ m∠ACD = 180° - 2xConsider ΔBEC
Since BE = EC, the opposite angles are congruent:
∠BCE ≅ ∠CBEThen:
m∠CBE = m∠BCE = xFind the angle BEC:
m∠BEC = 180° - (x + x) = 180° - 2xComparing the above we see that:
m∠BEC = m∠ACDprovedfind the probability of picking a red marble and a green marble when 2 marbles are picked (without replacement)from a bag containing 6 red and 6 green marbles.}
Answers
p = 6/11.
So we have a bag that contains 6 red marbles and 6 green marbles.
Then the total number of marbles that are in that bag is:
6 + 6 = 12
There are 12 marbles in the bag, and we assume that all marbles have the same probability of being randomly drawn.
Now we draw two marbles, we want to find the probability that one is red and the other is green.
The first marble that we draw does not matter, as we just want the second marble to be of the other color.
So, suppose we draw a green one in the first attempt.
Then in the second draw, we need to get a red one.
The probability of drawing a red one will be equal to the quotient between the red marbles in the bag (6) and the total number of marbles in the bag (12 - 1 = 11, because one green marble was drawn already)
Then the probability is:
p = 6/11.
Notice that would be the exact same case if the first marble was red.
Then we can conclude that the probability of getting two marbles of different colors is:
p = 6/11.
Someone plz help me on this
Answers
Answer:
9²+x²=13²
81+x²=169
x²= 169-81
x²=88
X= 9.38
x=9.4[tex]x = \sqrt{88} [/tex]
i need help asap im timed
Answers
Answer:-
Refer to attachment for the required solution.
Answer:
Step-by-step explanation:
Geometry, please answer question ASAP
Answers
Answer:
It's 5 which is A.
Step-by-step explanation:
Yesterday, the snow was 2 feet deep in front of Archie’s house. Today, the snow depth dropped to 1.6 feet because the day is so warm. What is the percent change in the depth of the snow?
The percent change in the depth of snow from yesterday to today is
%.
Answers
100% - 80% = 20%
So the snow depth decreased 20%.
Help pls, I need Help :D
Answers
5
Step-by-step explanation:
Step 1. Get two points off the graph
Points: (-70, 0) and (-60, 50)
Step 2. Use the two points to find the slope
m = slope
m = change in y/change in x
m = y2 - y1/x2 - x1
m = 50 - 0/-60 - -70
m = 50/10
m = 5/1
m = 5
The slope is 5
Pleeeeeeeeaaaaaaaaaaaasse help 71 points!!!!!!!!!
Answers
Answer:
54
Step-by-step explanation:
The perimeter is the sum of the outside
P = 8+4+5+10+( 4+10) +(8+5)
P = 54
the Marked price of a book is rupees 500 if 30% discount is all over there in a loss of rupees hundred is made what is the cost price of the book
Answers
Answer:
cost price of book is Rs. 570
Pls help. I really suck at math.
Determine whether the following polygons are similar.
Answers
Answer:
They are not similar.
To easily check if they are similar, you only need to look at the degrees angles, since if the angles are the same, the lengths of the sides will always come out to be similar somehow.
Those triangles possess right angles as you can see the little square thingie in the corners.
Those are 90 degrees, and you can add the 30 degrees in the left shape to 90 to get 120.
There are 180 degrees in a triangle, so 180 - 120 = 60.
Therefore, the unknown angle is 60.
A 30 60 90 triangle is called a special right triangle since there are many useful ratios hidden inside.
The other triangle has a 55 degree angle which is not on the first, so they must not be similar.
Pls brainly dont delete this link, its useful.
https://blog.prepscholar.com/30-60-90-triangle-ratio-formula
This helps you understand the special triangles.
You don't suck at math, you suck at geometry imo, though only in this unit of geometry, probably good at others.
Step-by-step explanation:
Shelly charges $10 per hour for her babysitting servives. Last month Shelly babysat for 15 hours. This month she babysat for n hours.
a. Write an expression using parentheses to describe how much money she made.
b. Given that n=12, evaluate your expression using the distributive property.
Answers
Answer:
A. 10(15) + 10n = $ made for babysitting
B. $270
Step-by-step explanation:
B. 10(15) + 10(12)
150 + 120 = $270
Plzz help me with this question my class test is going on
Answers
Step-by-step explanation:
2x+3y+5+4x-7y-8
2x+4x+3y-7y+5-8
6x-4y-3
Answer:
6x - 4y - 3
Step-by-step explanation:
They are basically telling you to sum both equations. So,
(2x + 3y + 5) + (4x - 7y - 8)
= 2x + 4x + 3y - 7y + 5 - 8
= 6x - 4y - 3
Find the missing angle. Round your answer to the nearest tenth. PLS HURRY.
Answers
Answer:
x = 24.4°
Hope this helps... Have a good day!!
Staff
Americans eat 7 billion hot dogs between Memorial Day and Labor Day. If all these hot dogs were laid end to end they
would circle the earth 21.5 times. If the circumference of the Earth is approximately 24,860 miles, and one mile is
5,280 feet, find the length (in inches) of each hot dog. (Round your answer to the nearest tenth)
Answers
Answer:
The length of each hot dog is 0.5000 inches.
Step-by-step explanation:
Total number of hot dogs eaten = 7 000 000 000
Circumference of the earth = 24 860 miles
21.5 times the circumference of the Earth = 21.5 x 24 860 miles
= 534490 miles
But,
1 mile = 5280 feet
So that,
534490 miles = X
X = 5280 x 534490
= 287707200 feet
Also,
1 feet = 12 inches
Then,
287707200 feet = Y
Y = 12 x 287707200
= 3452486400 inches
Thus,
the length of each hot dog = [tex]\frac{3452486400}{7000000000}[/tex]
= 0.4932
The length of each hot dog is 0.5000 inches.
Instructions: Find the value of the trigonometric ratio. Make sure to
simplify the fraction if needed.
С
32
40
B
24
A
Tan C =
Answers
Answer:
tanC will be given by the opposite over the adjacent
tanC=24/32
simplified to 6/8
I hope this helps
What is the surface area of a sphere with a diameter of 14 cm?
1961 cm2
287 cm2
7841 cm2
981 cm2
Answers
Answer:
??
Step-by-step explanation:
how
did you get 616? are you even looking at the 4 answers?????
If a ray bisects a right angle, then each newly formed angle measures 45 degrees.
A) Sometimes
B) Always
C) Never
Answers
This is because ‘bisect’ means to spilt exactly in half. If you split 90 degrees in half, you get 45 degrees.
Hope this helps!
Answer:
Always
Step-by-step explanation:
Bisects means to divide in half
90/2 = 45
So the angles are each 45 degrees
Last night, the two dinner specials at Will's favourite restaurant were salmon fillet and steak. The restaurant served 15 salmon fillets and 5 steaks. What percentage of the specials served were salmon fillets?
Answers
Answer:
75% of the specials served were salmon fillets
Step-by-step explanation:
We have that:
15 + 5 = 20 specials were served.
Of those, 5 were salmon fillets.
What percentage of the specials served were salmon fillets?
15*100%/20 = 75%
75% of the specials served were salmon fillets
find the ratio between 6 cm and 1.5m
Answers
Answer:
6:150
Step-by-step explanation:
If you like my answer mark me brainliest
Answer:
1:25
Step-by-step explanation:
1.5m=150cm
6:150
1:25
What is the equation of the line that passes through the points (–12, –8) and (–17, –16)?
Answers
Answer:
firstly find the gradient given by the equation
m=y2-y1/x2-x1
in this case x1 is -12,x2 is -17, y1 is -8 and y2 is-16
m=-16+8/-17+12
=-8/-5 or1.6
then use the equation
y-y1=m(x-x1)
y+8=1.6(x+12)
y+8=1.6x+19.2
y=1.6x+11.2
I hope this helps and sorry if it's wrong
(4y¹²) (3y)
Please help me
Answers
PLZ HELP ME ASAP PLZZ
Answers
Answer:
helloo thereeee
we do such construction from a making bc arc then from b and c making x just when we need to make
Angle bisector
hope that helps ig :)
Please answer this!!
Answers
Answer:
BC = 6.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta =opp /adj
tan C = AB / BC
tan 45 = 6.8/ BC
BC = 6.8 / tan 45
BC = 6.8 / 1
BC = 6.8
Answer: Choice D. 6.8
Step-by-step explanation:
45,45,90 triangles, memorize that the short sides are equal to each other in length and are [tex]\frac{1}{\sqrt{2} }[/tex] the length of the long side.
The function f(c)=95c+32 is used to convert temperatures from Celsius, c, to Fahrenheit, f(c). What is the temperature in Fahrenheit when it is 22° Celsius? Round your answer to the nearest integer. A 40° B 54° C 72° D 97°
Answers
C 72°
Answer:
we have
f(c)=9/5C+32
now
22°C to °F
°C=22°
we have
f(c)=9/5C+32
f(c)=9/5*22+32=71.6≈72
answer is
22°C=72°F
Answer: [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boldsymbol{72^\circ F}[/tex]
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol{} f(c)=\frac{9}{5} c+32 \ \ in \ \ our \ \ case \\\\\\\\f(22)=\frac{9\cdot 22}{5} +32=39,6+32=7\underline1,6\approx72^\circ F[/tex]
