The values of constants a and b so that lim x -x2-1-x-1-a x-b-1-2- areA- a-1- b-3-2B- a-0- b-0C- a-2- b-1D- a-1- b-3-2

The correct option is D x→∞lim ( x^2+1/x+1 ax b )=1/2 ⇒x→∞lim(x^2+1) (ax+b)(x+1)/x+1=1/2 ⇒x→∞limx^2(1 a) (a+b)x b+1/x+1=1/2 ⇒ 1 a=0 and a+b= 1/2 ∴ a=1 b= 3/2 ...

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Standard XI

Mathematics

Continuity of a Function

The values of...

Question

$The values of constants a and b so that l i m x \to \infty (\frac{x^{2} + 1}{x + 1} - a x - b) = \frac{1}{2}, a r e$

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Solution

The correct option is A

$l i m x \to \infty (\frac{x^{2} + 1}{x + 1} - a x - b) = \frac{1}{2} \Rightarrow l i m x \to \infty \frac{(x^{2} + 1) - (a x + b) (x + 1)}{x + 1} = \frac{1}{2} \Rightarrow l i m x \to \infty \frac{x^{2} (1 - a) - (a + b) x - b + 1}{x + 1} = \frac{1}{2} \Rightarrow 1 - a = 0 a n d a + b = - \frac{1}{2} ∴ a = 1 b = - \frac{3}{2}$

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