Functions Question 442
Question: If $ f(x),=, \begin{cases} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x} & \text{,for}-1\le x<0 \\ 2x^{2}+3x-2 & \text{,},\text{for },0\le ,x\le 1 \\ \end{cases} . $ , is continuous at $ x=0 $ , then $ k= $
[EAMCET 2003]
Options:
? 4
? 3
? 2
? 1
Show Answer
Answer:
Correct Answer: C
Solution:
L.H.L. $ =\underset{x\to {0^{-}}}{\mathop{\lim }},\frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}=k $ R.H.L. $ =\underset{x\to {0^{+}}}{\mathop{\lim }},(2x^{2}+3x-2)=-2 $ Since it is continuous at $ x=0 $, L.H.L = R.H.L = f(0) Þ $ k=-2 $ .
BETA
