Find the midpoint, M, of AB.
А
M
B
[?]
22

Answer:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}} \frac{x\ln x}{\tan x}=-\infty\implies \text{B. Nonexistent (best answer)}[/tex]

Step-by-step explanation:

Recall L'Hopital's rule:

[tex]\displaystyle \lim_{x\rightarrow c}\frac{f(x)}{g(x)}=\lim_{x\rightarrow c}\frac{f'(x)}{g'(x)}[/tex]

First derivative of [tex]x\ln x[/tex]:

Recall the product rule:

[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]

[tex]\displaystyle \frac{d}{dx} (x\ln x)=\frac{d}{dx}(x)\cdot \ln (x)+\frac{d}{dx}(\ln x)\cdot x[/tex]

Note that:

[tex]\displaystyle \frac{d}{dx}(x)=1,\\\frac{d}{dx}(\ln (x))=\frac{1}{x}[/tex]

Simplifying, we get:

[tex]\displaystyle \frac{d}{dx} (x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x,\\\frac{d}{dx}(x\ln x)=\ln x+1[/tex]

First derivative of [tex]\tan x[/tex]:

[tex]\displaystyle \frac{d}{dx}(\tan x)=\sec^2 x[/tex]

Therefore, we have:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}[/tex]

By definition, [tex]\cos x=\frac{1}{\sec x}[/tex]. Therefore,

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}=\lim_{x\rightarrow 0^{+}}\cos^2x(\ln x+1)[/tex]

Note:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\cos^2x=1,\\\lim_{x\rightarrow 0^{+}}\ln x+1=-\infty[/tex]

Substitute:

[tex]\displaystyle \lim_{x \rightarrow0^{+}} \cos^2x(\ln x+1)=1\cdot (-\infty)=-\infty[/tex]

Therefore, we have:

[tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty \text{}[/tex], which best corresponds with [tex]\boxed{\text{B. Nonexistent}}[/tex]

*Commentary:

Technically speaking, a limit exists only if it is equal to a real number. By proper definition, infinity is not a number. With that being said, you will see limits expressed as infinity or negative infinity.

Here's what I will say about this specific problem.

The problem is stipulating that we approach [tex]x[/tex] from the right side. Because of this condition, it may be unorthodox to say this limit doesn't exist. However, if the problem just asked for [tex]\displaystyle \lim_{x\rightarrow 0}\frac{x\ln x}{\tan x}[/tex], it is common and preferred to say this limit does not exist, since [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{x\ln x}{\tan x}\neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}[/tex].

For example, [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}=\text{DNE}[/tex], because [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}[/tex] diverges. In other words, [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{1}{x}=-\infty \neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{1}{x}=\infty[/tex].

But again, the problem is asking for the limit as [tex]x[/tex] approaches from the right, in which case [tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty }[/tex]. It's really a pedagogical choice whether to say a limit equal to infinity or negative infinity exists or not since infinity implies there is no limit, so saying the limit of something is infinity becomes an oxymoron. In this case, the person who wrote the answer choices chose to express a limit of infinity as nonexistent, but it is worth mentioning that someone else solving this problem might express [tex]-\infty[/tex] as the answer, and they would be just as, if not more, correct.

Without resorting to L'Hopital's rule, recall that

[tex]\displaystyle \lim_{x\to0}\frac{\sin(ax)}{ax} = 1[/tex]

for a ≠ 0. Then

[tex]\displaystyle \lim_{x\to0^+} \frac{x \ln(x)}{\tan(x)} = \lim_{x\to0^+}\frac x{\sin(x)} \times \lim_{x\to0^+}\cos(x) \times \lim_{x\to0^+}\ln(x)[/tex]

The first two limits exist and are equal to 1, but the last limit is -∞.

Hey there!

The formula to find the perimeter of a rectangle is "P=2(l+w)".

Hope this helps!

Have a great day! :)

Answer:

formula to find the perimeter of rectangle is

hope it helps

stay safe healthy and happy.

Answer:

[tex]\frac{1}{30}[/tex]

Step-by-step explanation:

Take it in steps. First, find 7/9+6. Then we'll find 8+6/3, and, finally, we'll divide the two answers.

1:

7/9+6 = 7/15

2:

8+6/3 = 14/3

3:

[tex]\frac{\frac{7}{15}}{\frac{14}{3}}[/tex] or [tex]\frac{7/15}{14/3}[/tex]

Then take that in chunks: 7/14 and 15/3.

7/14 = 1/2

15/3 = 5/1

Use those to rewrite it as [tex]\frac{1/5}{2/3}[/tex].

1/5 = .2

2/3 ≈ .6667 so we'll keep writing it as 2/3

[tex]\frac{\frac{.2}{2}}{3}[/tex]

.2/2 = .1, so:

[tex]\frac{.1}{3}[/tex] = [tex]\frac{1}{30}[/tex]

Answer:

Answer:

If:   153  words = 3  minutes  :

Then:  1 minute =  153 3 =  51 words

10 minutes is:

10 × 51 = 510

Ben can type 510 words in 10 minutes

It's likely that curve A is f and curve B is f '.

The points where curve B crosses the horizontal axis correspond to the extrema of curve A at around 0 and 0.45, and the extremum of curve B corresponds to the inflection point of curve A at around 0.2. These observations are consistent with the first and second derivative tests.

9514 1404 393

Answer:

  3 in

Step-by-step explanation:

Ratios of corresponding sides are equal, so we have the proportion ...

  x/(5 in) = (6 in)/(10 in)

  x = (5 in)(6/10) = 3 in

The missing side (x) is 3 in.

Answer:

y = c1 e^-x + c2 e^(3x)

Step-by-step explanation:

Review linear DE's

(D-3)(D+1)y = 0

I think the answer is A and C!

Answer:

B) Keeping A constant and decreasing B

C) Increasing A and keeping B constant

Step-by-step explanation:

I did it on Khan Academy :)

Answer:

a. isosceles

b. isosceles

c. scalene

Answer:

98376

Step-by-step explanation:

Answer:

A = W² + 6W

Step-by-step explanation:

The width is W.

The length is 6 units greater than the width, so the length is W + 6.

The area is the product of the length and width.

A = (W + 6)W

A = W² + 6W

Answer:

x=10

Step-by-step explanation:

10 a 8 son dos, entonces 14 ax es 4

Answer:

La explicación sería:

//////////////////////////

=> 9 * 2 + 4/2 = 20

=> 18 +2 =20

=> 20 =20

//////////////////////////

=> 5*2 + 8/2 = 14

=> 10 +4 =14

=> 14 =14

//////////////////////////

=> 3*2 + 10/2 = x

=> 6 + 5 = x

=> 11 = x

9514 1404 393

Answer:

  (B)  Function 2

Step-by-step explanation:

We can compute the slope of Function 2 using the slope formula.

  m = (y2 -y1)/(x2 -x1) . . . . where x and y are the independent and dependent variables.

  m = (0.2 -0.8)/(3 -2) = -0.6

The slope of Function 1 is about ...

  -3/7 ≈ -0.43

The slope of Function 2 is more negative.

__

On a graph, the line representing function 2 has a steeper downward slope.

Answer:

25d + 100

Step-by-step explanation:

I will call "d" the days passed

25d + 100

Answer:

ok dude

Step-by-step explanation:

Wʜᴇʀᴇ ɪs ǫᴜᴇsᴛɪᴏɴ?

Answer:

what help l don't understand please sorry I didn't help you explain your problem l will help you

300000000000000000000000

Step-by-step explanation:

[tex]w = x^4\sin(y^4z^3)[/tex]

The differential [tex]dw[/tex] is

[tex]dw = 4x^3\sin(y^4z^3)dx [/tex]

[tex]\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(4y^3z^3)dy [/tex]

[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(3y^4z^2)dz[/tex]

Answer:

x>10  or x< -2

Step-by-step explanation:

There are two solutions, one positive and one negative, remembering to flip the inequality for the negative

x-4 >6    or x-4 < -6

Add 4 to each side

x-4+4 > 6+4   or x-4+4 < -6+4

x>10  or x< -2

Answer:

B two congruent pieces

Step-by-step explanation:

Perpendicular means at a 90 degree angle

bisector means it divides in it half, into two equal pieces

You are falling by [tex]32[/tex],

[tex]128, 128 - 32, 128 - 32\cdot2,\dots[/tex]

In general your sequence is defined as,

[tex]a_n=128-32\cdot n[/tex] where [tex]0\leq n \lt\infty[/tex].

The question is at which [tex]n[/tex] does the value [tex]a_n=0[/tex].

If you divide [tex]128[/tex] with [tex]32[/tex] you get the number of steps needed to stuff [tex]128[/tex] with [tex]32[/tex], [tex]4[/tex].

If you plug in [tex]n=4[/tex], you get [tex]a_4=128-32\cdot4[/tex], since [tex]32\cdot4=128[/tex] you get [tex]a_4=0[/tex].

The zero turn of the arithmetic sequence is thus at [tex]n=4[/tex].

Hope this helps :)

jet1 = 549 mi/h

jet2 = 620 mi/h

x= jet1

x + 71 = jet2

6 hours

6 * x

6 * x + 71

6x + 6x + 426 = 7014

12x = 7014 - 426

12x = 6588

x = 6588/12

x= 549

x + 71 = 620

wyzant

Answer:

Step-by-step explanation:

P ___15cm______T____10cm______B

As shown above,

PB is a line segment and point T in it forming - PT = 15 and TB = 10

So,

PB = PT + TB

= 15 + 10

= 25 (Ans)

PEMDAS- Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Answer= -91

Answer:

The most basic question I have ever seen lol

XY = 9*3 = 27

Answer:

6(3) - 4 - 3²

Step-by-step explanation:

(g - f) = 6x - (4 - 2x²)

= 6x - 4 - 2x²

and when we replace x with 3 ,it will be

6(3) - 4 - 3²

hope this helps

Answer:

Basically what the person on top of me said

Step-by-step explanation:

Got it right !

Answer:

$127.875

Step-by-step explanation:

cost of 3 pizzas= $15*3

cost of 3 pizzas=$45

cost of 15 drinks=$1.50*15

cost of 15 drinks=$22.5

cost of 6 nachos=$5.80*6

cost of 6 nachos=$34.8

Total cost = pizza cost+ drinks+nachos

total cost=$45+$22.5+$34.8

total cost=$102.3

Now ,

Tip cost=$102.3*20%

=$20.46

tex cost=$102.3*5%

=$5.115

Bill which all friends pay=total cost+ tip cost+tex cost

= $102.3+$20.46+$5.115

=$127.875

Answer:

b

Step-by-step explanation:

Answer:

(0.5, -1)

Step-by-step explanation: