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

 Exercise

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

 

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

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

 

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

$\frac{\infty -2\cdot \infty +2}{\infty -1}- \infty $

 

Any expression multiplied by infinity tends to infinity, in other words: $\infty\cdot(\pm n)=\pm\infty$, if $n\neq0$

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

 

Infinity minus infinity is an indeterminate form

indeterminate

indeterminate

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