If f(x) , = , * 20 c 1 + kx - 1 - kx x & ,for - 1 x < 0 2 x^2 + 3… - Vidyadip

MCQ

If $f(x)\, = \,\left\{ {\begin{array}{*{20}{c}}{\frac{{\sqrt {1 + kx} - \sqrt {1 - kx} }}{x}}&{{\rm{,for}} - 1 \le x < 0}\\{2{x^2} + 3x - 2}&{{\rm{,}}\,{\rm{for\,\, }}\,0 \le \,x \le 1}\end{array}} \right.$, is continuous at $x = 0$, then $k = $

A
$-4$
B
$-3$
✓
$-2$
D
$-1$

✓

Answer

Correct option: C.

$-2$

c
(c) $L.H.L.$ $ = \mathop {\lim }\limits_{x \to {0^ - }} \frac{{\sqrt {1 + kx} - \sqrt {1 - kx} }}{x} = k$

$R.H.L.$ $ = \mathop {\lim }\limits_{x \to {0^ + }} (2{x^2} + 3x - 2) = - 2$

Since it is continuous,

$L.H.L = R.H.L$ ==> $k = - 2$.

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