Practicing Success
The value of $\underset{x→∞}{\lim}(\frac{x^2+1}{x+1}-ax-b)=0$, then:
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a = 1, b = -1 a = -1, b = 1 a = 1, b = 1 a = b = 0 |
a = 1, b = -1 |
$\underset{x→∞}{\lim}(\frac{x^2+1}{x+1}-ax-b)=0$ It is a (∞ - ∞) form, first convert it in to $(\frac{∞}{∞})$ form. $\underset{x→∞}{\lim}\frac{x^2+1-ax(x+1)-b(x+1)}{x+1}=\underset{x→∞}{\lim}\frac{(1-a)x^2-(a+b)x+(1-b)}{x+1}$$[\frac{∞}{∞}form]$ On differentiating numerator and denominator, we get : $\underset{x→∞}{\lim}\frac{2(1-a)x-(a+b)}{1}=0$ On comparing both sides, we get : 1 - a = 0 and a + b = 0 a = 1 and b = -a Hence, a = 1 and b = -1 |