Functions Question 3
Question: If $ \underset{x\to 0}{\mathop{\lim }}kxcosecx=\underset{x\to 0}{\mathop{\lim }}xcosec\ kx $ , then $ k= $
Options:
A) 1
B) -1
C) $ \pm 1 $
D) $ \pm 2 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to 0}{\mathop{\lim }}kx\cos ecx=\underset{x\to 0}{\mathop{\lim }}x\cos eckx $
$ \Rightarrow k.\underset{x\to 0}{\mathop{\lim }}\frac{x}{\sin x}=\frac{1}{k}\underset{x\to 0}{\mathop{\lim }}\frac{kx}{\sin kx} $
$ \Rightarrow k=\frac{1}{k}\Rightarrow k=\pm 1 $ .
BETA
