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Problem

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

01:15

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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 37 Hard Difficulty

Find the limits.
$$
\lim _{x \rightarrow+\infty}\left[x-\ln \left(x^{2}+1\right)\right]
$$

Answer

$$\lim _{x \rightarrow+\infty}\left[x-\ln \left(x^{2}+2\right)\right]=+\infty$$

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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Watch More Solved Questions in Chapter 3

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Video Transcript

So we're starting with a limit as X goes to infinity of X minus natural log X squared plus one. And if we just try to evaluate this limit, we noticed that we get infinity minus infinity. Okay. In particular, this natural log X squared plus one is going to infinity because the X squared plus ones going to infinity. And so the natural log of that is going to So we haven't indeterminant for infinity minus infinity. We'll need to somehow rewrite this as a fraction in order to get anywhere. So let's go ahead and rewrite. The X is a fraction or excuse me, rewrite X using natural log so we can rewrite it as natural log of eat the X And now we can go ahead and use our log properties, and here we can go ahead. And because natural log is a continuous function, we can interchange the natural log in the limit sign. So we've natural log with limit of X to infinity e to the X, divided by X squared plus one. And now here, if we try to take this limit on the on the inside of the parentheses, um, we end up getting infinity over infinity. But it's since it's a fraction we can go ahead and use low petals rule. Okay, we're in the same sort of situation. Infinity over infinity. Let's go ahead and use low petals rule. And here we see that the limit on the inside is now going to infinity. So our answer here as infinity, 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

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Find $f^{\prime}(x)$
$$
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$$

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