Find the limit of 1+(ln(x+1)^2)/x as x approaches infinity

 Exercise

$\lim_{x\to\infty}\left(1+\frac{ln\left(x+1\right)^2}{x}\right)$

 

Evaluate the limit $\lim_{x\to\infty }\left(1+\frac{\ln\left(x+1\right)^2}{x}\right)$ by replacing all occurrences of $x$ by $\infty $

$1+\frac{\ln\left(\infty +1\right)^2}{\infty }$

 

Infinity plus any algebraic expression is equal to infinity

$1+\frac{\ln\left(\infty \right)^2}{\infty }$

 

The natural log of infinity is equal to infinity, $\lim_{x\to\infty}\ln(x)=\infty$

$1+\frac{\infty ^2}{\infty }$

 

Infinity to the power of any positive number is equal to infinity, so $\infty ^2=\infty$

$1+\frac{\infty }{\infty }$

 

Infinity divided by infinity ($\frac{\infty}{\infty}$) is an indeterminate form

indeterminate

indeterminate

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