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Differential Calculus> Find the value of a & b such that lim (x ...

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

Lovey , 10 Years ago

Grade 12

2 Answers

Jitender Singh

Last Activity: 10 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

Last Activity: 10 Years ago

Thank you Jitender Singh Sir for the quick response.

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