find-the-limits-lim-_x-rightarrow-infty-x1-ln-x

Name: find the limits lim _x rightarrow infty x1 ln x
Uploaded: 2020-04-19
Duration: 58 s
Channel: Numerade
Description: Find the limits $$\lim _{x \rightarrow \infty} x^{1 / \ln x}$$

Question

Find the limits $$\lim _{x \rightarrow \infty} x^{1 / \ln x}$$

Ahmed Ibrahim · Accepted Answer

in In this equation, we can take if off x equals tow x our one over in eggs. So if we took land off X, we can get men Ex Land X, which is equal to one. Therefore, if we took now limits necks approaches to affinity for our function. If you fix, we can write it as, uh, expansion e then therefore X. And we just told that Len FX Andi, it&#x27;s equal to one so we can write it as e one, which is our solution equal to E. Thank you.

Ahmed Ibrahim · Answer

this question. We can say that f X equals to lend ex old or one over X. So, Len FX, if we took land off X Yeah, April fix will be equal toe Len off. Len. Sorry. Um, four Len x or yes. Now, if we took lam it when x approaches store affinity for our land FX So we will get Yeah. Oh, men, eggs over eggs if we took a derivative So we will have won over X then x or one if we have secured X by infinity. So we have one over M planet Yuji. 0 0/1 will be equal to zero. Therefore, um, limit X approaches toe affinity for our function of X way. Can&#x27;t write it as limit extends to affinity e for Len. Oh, it&#x27;s trying to gain, then. Well, thanks. And our land f of X as we just solve it equal to zero. So we have a poor zero, which is equal to one. Our final solution. Thank you.

Zachary Mitchell · Answer

So we&#x27;re looking at the limit as X goes to it. Positive infinity of natural log of X raised to the one over X. Let&#x27;s set that equal toe l Now let&#x27;s take the limit. Excuse me. The natural log of each side. Okay. And our next step is to interchange the limit with the natural log. And we can do this because natural log. It&#x27;s continuous. Okay, let&#x27;s go ahead and use our log property to bring that one that one over X down. So now we have natural log of natural. Lagerback&#x27;s divided by X. And if we try to evaluate this limit, we get infinity over infinity. So we&#x27;re set up to use low petals rule. Let&#x27;s go ahead and do that. So the derivative, the top is one over. Natural log X times one over X by chain room to remove. The bottom is just one. Okay. And this limit is something that we can easily evaluate. Zero. Okay, so we have that The natural log of LZ zero. This implies that l is equal to one. That&#x27;s it. We&#x27;re done

Zachary Mitchell · Answer

So we&#x27;re starting with limit as X goes to positive infinity of natural log of X, divided by X. Now, if we just go in and try to do this limit well, on the numerator, we get infinity on the denominator. We get infinity, we have infinity over infinity. That&#x27;s an indeterminant form. And we&#x27;re good to go to use low petals rule. I&#x27;m going to write LH over this equal sign indicating that we are using Low Patel&#x27;s role in the next step so that the root of the numerator natural Lagerback&#x27;s is going to be one over X and the derivative of the denominator X is one. Okay, and this new limit that we have could be evaluated. We&#x27;re done.

Ahmed Ibrahim · Answer

this question. We can take FF X equal tow X our negative one overland X So if we took Len eggs, we can get negative then X over next, which is equal to negative one. Therefore, if we took lam it when X approaches to issue for our farms and who fix, we can write it as e or Glenn If we fix and lend FX. We just told with as negative one. So it would be people negative corn, which is equal or former solution e one over Thanks.

Zachary Mitchell · Answer

here. We&#x27;re starting with a limit as X goes to infinity, the natural log of X minus natural log of one plus X. And if we try to evaluate this limit right away noticed that we get infinity minus infinity. So we&#x27;re gonna go ahead and rewrite this. Let&#x27;s go ahead and use our log properties. Okay, so now we have just ah, natural log here, and we&#x27;re going to go ahead and use our limit interchange property that says that we can interchange the natural log with the limit because the natural log is a continuous function. Okay. And now here were set up to use low petals. Role because we have on infinity over infinity, huh? Form. So let&#x27;s go ahead and use lot. Hotels rule the derivative of the numerator. Pecs is one. And the derivative of the denominator is one. Okay, so we get natural. Look of one that&#x27;s equal to zero. That&#x27;s your answer.

Problem

Find the limits $$\lim _{x \rightarrow \infty}(1+…

Problem 56 Easy Difficulty

Find the limits $$\lim _{x \rightarrow \infty} x^{1 / \ln x}$$

Answer

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Joel Hass, Christopher Heil, Przemyslaw Bogacki

University Calculus: Early Transcendentals

Grace H.

Catherine R.

Anna Marie V.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

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University Calculus: Early Transcendentals

Grace H.

Catherine R.

Anna Marie V.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Joel Hass, Christopher Heil, Przemyslaw BogackiUniversity Calculus: Early Transcendentals

Grace H.

Catherine R.

Anna Marie V.

Kristen K.

Joel Hass, Christopher Heil, Przemyslaw Bogacki

University Calculus: Early Transcendentals