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# Find the limit of $\frac{\ln\left(x\right)}{\sqrt{x}}$ as $x$ approaches $\infty$

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##  Step-by-step Solution 

Problem to solve:

$\lim_{x\to\infty }\left(\frac{\ln\left(x\right)}{\sqrt{x}}\right)$

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Plug in the value $\infty$ into the limit

$\frac{\ln\left(\infty \right)}{\sqrt{\infty }}$

Learn how to solve limits to infinity problems step by step online.

$\frac{\ln\left(\infty \right)}{\sqrt{\infty }}$

Learn how to solve limits to infinity problems step by step online. Find the limit of (ln(x)/(x^1/2) as x approaches infinity. Plug in the value \infty into the limit. The natural log of infinity is equal to infinity, \lim_{x\to\infty}\ln(x)=\infty. Infinity to the power of any positive number is equal to infinity, so \sqrt{\infty }=\infty. Evaluate the limit \lim_{x\to\infty }\left(\frac{1}{\frac{1}{2}\sqrt{x}}\right) by replacing all occurrences of x by \infty .

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##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Limits by direct substitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing

### Main topic:

Limits to Infinity

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