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  • <img alt="\text{If}\lim _{x \rightarrow \infty}\left(\frac{x^{2}+1}{x+1}-a x-b\right)=\infty\: ,\text{find\; a and b}" src="/latex-image/?%5Ctext%7BIf%7D%5Clim%20_%7Bx%20%5Crightarrow%20%5Cinfty%7D

\text{If}\lim _{x \rightarrow \infty}\left(\frac{x^{2}+1}{x+1}-a x-b\right)=\infty\: ,\text{find\; a and b}.

Option: 1

a=1, b=1


Option: 2

a=1, b \neq 1


Option: 3

a \neq 1 ; b = 1


Option: 4

a \neq 1, b \in R


Answers (1)

best_answer

\lim _{x \rightarrow n}\left(\frac{x^{2}+1}{x+1}-a x-b\right)=\infty
 

\Rightarrow \quad \lim _{x \rightarrow \infty} \frac{\left[(1-a) x^{2}-(a+b) x+1-b\right]}{(x+1)}=\infty

The limit of the given expression will be infinity, if degree of numerator is more than that of denominator.

\therefore \quad 1-a \neq 0 \Rightarrow a \neq 1

Hence, a \neq 1 and b can assume any real value.

Posted by

Gaurav

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