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

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

Option: 1

a=1, b=-3


Option: 2

a=3, b=1


Option: 3

a=-1, b=-3


Option: 4

a=1, b=3


Answers (1)

best_answer

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

Since, the limit of the given expression is a finite , non-zero number, therefore numerator and denominator are of the same degree.

\therefore (1-a)=0 \Rightarrow a=1

\lim _{x \rightarrow \infty} \frac{0-(a+b) x+1-b}{x+1}=-(a+b)=2
a+b=-2 \Rightarrow b=-3

So, a=1, b=-3

Posted by

Rakesh

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