Differentiation Question 206
Question: If $ \underset{x\to a}{\mathop{\lim }}[ \frac{f(x)}{g(x)} ] $ exist, then which one of the following correct-
Options:
A) Both $ \underset{x\to a}{\mathop{\lim }}f(x) $ and $ \underset{x\to a}{\mathop{\lim }}g(x) $ must exist
B) $ \underset{x\to a}{\mathop{\lim }}f(x) $ need not exist but $ \underset{x\to a}{\mathop{\lim }}g(x) $ must exist
C) Both $ \underset{x\to a}{\mathop{\lim }}f(x) $ and $ \underset{x\to a}{\mathop{\lim }}g(x) $ need not exist
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ f(x)=x,g(x)=\frac{1}{x} $
$ \underset{x\to 0}{\mathop{\lim }}f(x)=0,\underset{x\to 0}{\mathop{\lim }}g(x)= $ does not exist But $ \underset{x\to 0}{\mathop{\lim }}[ \frac{f(x)}{g(x)} ]=\underset{x\to 0}{\mathop{\lim }}[ x^{2} ]=0 $ Hence, none of these is only true option.
BETA
