Find the limit of (x^6+x^2+1)^(1/2)-(x^6+x^3-x)^(1/2) as x approaches infinity

 Exercise

$\lim_{x\to\infty}\left(\sqrt{x^6+x^2+1}-\sqrt{x^6+x^3-x}\right)$

 

Evaluate the limit $\lim_{x\to\infty }\left(\sqrt{x^6+x^2+1}-\sqrt{x^6+x^3-x}\right)$ by replacing all occurrences of $x$ by $\infty $

$\sqrt{\infty ^6+\infty ^2+1}-\sqrt{\infty ^6+\infty ^3- \infty }$

 

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

$\sqrt{\infty +\infty +1}-\sqrt{\infty ^6+\infty ^3- \infty }$

 

Infinity to the power of any positive number is equal to infinity, so $\infty ^6=\infty$

$\sqrt{\infty +\infty +1}-\sqrt{\infty +\infty ^3- \infty }$

 

Infinity to the power of any positive number is equal to infinity, so $\infty ^3=\infty$

$\sqrt{\infty +\infty +1}-\sqrt{\infty +\infty - \infty }$

 

Infinity minus infinity is an indeterminate form

indeterminate

indeterminate

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