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Numerade Educator

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Problem 19 Easy Difficulty

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

$ \displaystyle \lim_{x\to \infty} \frac{\ln x}{\sqrt{x}} $

Answer

his limit has the form $\frac{\infty}{\infty} . \quad \lim _{x \rightarrow \infty} \frac{\ln x}{\sqrt{x}} \stackrel{\mathrm{n}}{=} \lim _{x \rightarrow \infty} \frac{1 / x}{\frac{1}{2} x^{-1 / 2}}=\lim _{x \rightarrow \infty} \frac{2}{\sqrt{x}}=0$

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Video Transcript

we need to find the following. Lim used her locked US rule and if possible, we can use some more. And you mentioned my mother. Okay, so this is a fraction First of thing to find the limit is plucking this number that isthe infinity. So if you do that, that has long infinity which is infinity divided by the square root ofthe infinity which is also infinity. So actually this way and saying determined form so we can use the locked US rule and this limit Hey, seek out a dynamic as axe goes to infinity the curative off the top which is one o r x divided by the d word half off about him which is ah half times X to the power ofthe minus. Huh? So we use the power ruled will find this the purity of off this one okay, And does some simply simplification, that is the ex goes to infinity. Ah, to here went over to one divided by one over True which was through and this is axe times for the boat Home is X times actually minus X the power of minus half which is X for the power off half So if axe goes to infinity, this one goes to infinity. And for the numerator, it is number. So a number divided by infinity. You get the name of his dear Oh.