Functions Question 254
Question: If $ f(x),=| ,\begin{matrix} \sin x & \cos x & \tan x \\ x^{3} & x^{2} & x \\ 2x & 1 & 1 \\ \end{cases} , | $ , then $ \underset{x\to 0}{\mathop{\lim }},\frac{f(x)}{x^{2}} $ is
[Karnataka CET 2002]
Options:
A) 3
B) ?1
C) 0
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=x(x-1)\sin x-(x^{3}-2x^{2})\cos x-x^{3}\tan x $ $ =x^{2}\sin x-x^{3}\cos x-x^{3}\tan x+2x^{2}\cos x-x\sin x $ Hence $ \underset{x\to 0}{\mathop{\lim }},\frac{f(x)}{x^{2}}=\underset{x\to 0}{\mathop{\lim }}( \sin x-x\cos x-x\tan x+2\cos x-. \frac{\sin x}{x} ) . $ $ =0-0-0+2-1=1 $ .
BETA
