First slide

Continuity

Question

$Value of ' a' if f (x) = \lim_{x \to \infty} \frac{a x^{2 n} + 2}{x^{2 n} + a + 1} is continuous of x = 1$

Moderate

A

$a = - 2 or - 1$
B

$a = - 3 or 2$
C

$a = - 2 or 1$
D

$a = 0 or - 1$

Solution

$For continuity at x = 1, a = \frac{2}{a + 1}$
$f (1^{+}) = a and f (1^{-}) = \frac{2}{a + 1}$
$\Rightarrow a^{2} + a = 2 \Rightarrow a^{2} + a - 2 = 0$ $\Rightarrow a = - 2 or 1$

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