find-the-limits-lim-_x-rightarrow-0-frac1-ln-xe1-x

Question

Find the limits.
$$
\lim _{x \rightarrow 0^{+}} \frac{1-\ln x}{e^{1 / x}}
$$

Zachary Mitchell · Accepted Answer

here we have the limits as X goes to zero from the positive side of one minus natural Log X divided by E to the one over X. Now, if we try to do this limit notice in the numerator, we&#x27;re going to get a positive infinity because the natural log by itself as a tends to zero from the right hand side equals negative infinity. So the numerator equals positive affinity the denominator We get a positive infinity. So we&#x27;ve infinity over infinity. That&#x27;s an indeterminant form and we can go ahead and use low Patel&#x27;s rule. We&#x27;re gonna write in hell h of this equal sign indicating that that&#x27;s what we do for this next step. Okay, so the derivative of the numerator is negative. One over X, the derivative the denominator. We&#x27;re gonna have to do a chain rule. Let&#x27;s see, So we get a negative X to the negative, too. Then we saw this and then this next step is simplifying. It simplifies here we get okay. And now this is a limit that weaken do because of the the numerator goes to zero. The denominator goes to infinity and that&#x27;s it

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

We&#x27;re starting with the limit as X goes to zero from the positive side of negative natural log X rays to the X. Let&#x27;s go ahead and assign that to variable L And then we&#x27;re gonna take the natural log of each side. And now, for our next step, we&#x27;re going to switch the natural log and the limit. And we can do this because natural August continuous. Okay? And so let&#x27;s go ahead and rewrite this thing as a fraction using the natural log properties so you can take that X and bring it down. Rewrite it as one over X. Okay, um, now, notice that the numerator does in fact make sense because, as zero has extends to zero from the positive side, natural law give extends to negative infinity. So we have the numerator attending to positive infinity on the top and the denominator tending to positivity on the bottom. So we&#x27;re good to go to use Lou petals rule. Let&#x27;s go ahead and do that one over a natural log X times negative one over X and then the denominator. We have negative one over X squared, and now we can simplify this. Um, and this works out to be negative. X over natural log X and this we can evaluate it. Zero Okay, so we have natural law. Go back and we have natural log of l is equal to zero. That implies that are limits. L is equal to one and we&#x27;re done.

Ahmed Ibrahim · Answer

in this question, we can take every X equal toe peep or explosives. Ex old power one over X. So lend 1/4 ex will be equals to Len E or Explosive likes Oh oh, you are cheese eggs. Now, if we took a limit when X approaches feel for our Len f off X, which is Len E X plus X over X, we can start by taking derivative. You will be equal toe e for X last one, people. Rex, I love sex. Now, if we substitute X by zero in this equation, we will get it. Pours the Roaches. 11 plus one is two who e poor zero is 11 plus zero is one. So this limit will be equal to zero said four We be cook lamb it x approaches zero for four eggs. We can write it as exponential then therefore X and we just saw it land ffx as too. So we have e post, which is 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

Ahmed Ibrahim · 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.

Problem

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

Problem 16 Easy Difficulty

Find the limits.
$$
\lim _{x \rightarrow 0^{+}} \frac{1-\ln x}{e^{1 / x}}
$$

Answer

$$\text { The limit is equal to } 0 .$$

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$$\text { The limit is equal to } 0 .$$

Calculus Early Transcendentals

Grace H.

Catherine R.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

Howard Anton, Irl Bivens, Stephen DavisCalculus Early Transcendentals

Grace H.

Catherine R.

Kristen K.

Michael J.

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals