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Find the value of a & b such that lim (x → inf) [((x 2 +1)/(x+1)) – (ax+b)] = 2

Find the value of a & b such that
lim (x → inf) [((x2+1)/(x+1)) – (ax+b)] = 2

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:Hello student, please find answer to your question
\lim_{x\rightarrow \infty }(\frac{x^{2}+1}{x+1}-ax-b) = 2
\lim_{x\rightarrow \infty }(\frac{x^{2}+1-(x+1)(ax+b)}{x+1}) = 2
\lim_{x\rightarrow \infty }(\frac{x^{2}+1-ax^{2}-bx-ax-b)}{x+1}) = 2
\lim_{x\rightarrow \infty }(\frac{x^{2}(1-a)-x(a+b)+(1-b)}{x+1}) = 2
\lim_{x\rightarrow \infty }(\frac{x^{2}(1-a)-x(a+b)}{x+1}) = 2
\Rightarrow 1-a = 0
\Rightarrow -a-b = 2
a = 1
b = 3
Lovey
10 Points
7 years ago
Thank you Jitender Singh Sir for the quick response.

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