Limits Continuity And Differentiability Question 99
Let f be a continuous function on R such that $ f\left(\frac{1}{4n}\right)=\left(\sin e^{n}\right)e^{-n^{2}}+\frac{n^{2}}{n^{2}+1} $ . Then the value of f (0) is
Options:
A) 1.
B) 1/2
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
As f is continuous. $ f(0)=\underset{x\to 0}{\mathop{\lim }}f(x)=\underset{n\to \infty }{\mathop{\lim }}f(1/4n) $
$ =\underset{n\to \infty }{\mathop{\lim }}( (\sin e^{n}){e^{-n^{2}}}+\frac{1}{1+1/n^{2}} )=0+1=1$
BETA
