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Problem

Find the limits. $$ \lim _{x \rightarrow+\infty}(…

02:22

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72

Problem 26 Hard Difficulty

Find the limits.
$$
\lim _{x \rightarrow \pi}(x-\pi) \cot x
$$

Answer

$$\lim _{x \rightarrow \pi}(x-\pi) \cot x=1$$

Related Courses

Calculus 1 / AB

Calculus Early Transcendentals

Chapter 3

TOPICS IN DIFFERENTIATION

Section 6

L Hopital's Rule; Indeterminate Forms

Related Topics

Functions

Limits

Derivatives

Differentiation

Continuous Functions

Applications of the Derivative

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Video Transcript

were starting with a limit as X goes to pie of X minus pi co tangents X. Now let's go ahead and rewrite this using the definition of co tensions. So we have X minus pi divided by sine of X Times Co sign of X and we know that we can go ahead and evaluate co sign of axe at pie and not some. And it's some non zero number. So let's go ahead and split this limit up into two different limits. Okay, then notice for this first limit, we have an indeterminant form of 0/0, and so we're going to apply loop atolls rule. The reason that we split up that these these products into two different limits is so that it would make the low petals rule easier. Otherwise, we'd have to deal with the product role when multiplying by a co sign. Okay, so let's go ahead and do low petals rule. The numerator is a one and the denominator is a co sign X. And then here we have the limits. His ex goes to pie off co sign X okay. And so we get one over negative one times negative one. That's just one. Our answer and that's it

We have video lessons for 84.11% of the questions in this textbook

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals

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Related Topics

Functions

Limits

Derivatives

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