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Q.

If $f (x) = K$ , for x=1 $= \frac{(9 x - 1) (\sqrt{x} - 1)}{3 x^{2} + 2 x - 5}$ , for $x \neq 1$ is continuous on $[0, \infty)$ , then K=______

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a

$\frac{1}{16}$

b

$\frac{1}{8}$

c

$\frac{1}{2}$

d

$\frac{1}{4}$

answer is D.

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Detailed Solution

$f (x)$ is continuous at $x = 1$
$∴ K = \underset{x \to 1}{l m t} \frac{9 x^{\frac{3}{2}} - 9 x - \sqrt{x} + 1}{3 x^{2} + 2 x - 5}$ by l’hospital rule
$K = \frac{\frac{27}{2} - 9 - \frac{1}{2}}{6 + 2} = \frac{1}{2}$ .

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