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Problem 21 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 0^+} \frac{\ln x}{x} $

Answer

$\lim _{x \rightarrow 0^{+}}[(\ln x) / x]=-\infty$ since $\ln x \rightarrow-\infty$ as $x \rightarrow 0^{+}$ and dividing by small values of $x$ just increases the magnitude of the
quotient $(\ln x) / x$. L'Hospital's Rule does not apply.

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Video Transcript

Okay, The questions for in the limit you still loved house rule. They're a proper rate. All may be a more elementary methods. So here this is the right hand limit because X goes to zero from the red hand off serial, here's a plus. So that means acts should be always positive and the V plucking zero plus in tow. This function we get line zero plus and we know that the graph ofthe long function is like this. So as X goes to zero from the right long ags goes to negative infinity. So that hope iss nagged him. He offended he be plucking zero plus and derided by eggs access zero plus, which is a very small positive number. So the top ISS a negative number vicious, very big and about home is a positive number, which is very small. So the answer The sign off the answer is negative. And here is a very big number divided by a small number, which is Marah Beak. So the answer is negative. Infinity Here we we don't use the laptop through a big house. This thing is not anything her in determined fall. So we cannot use the laptops rule here