Functions Question 34
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{x}{|x|+x^{2}}= $
Options:
A) 1
B) ?1
C) 0
D) Does not exist
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to 0-}{\mathop{\lim }},f(x)=\underset{h\to 0}{\mathop{\lim }},\frac{0-h}{h+h^{2}}=\underset{h\to 0}{\mathop{\lim }}\frac{-1}{1+h}=-1 $ and $ \underset{x\to 0+}{\mathop{\lim }},f(x)=\underset{h\to 0}{\mathop{\lim }},\frac{h}{h+h^{2}}=\underset{h\to 0}{\mathop{\lim }}\frac{1}{1+h}=1 $ Hence limit does not exist.
BETA
