Differentiation Question 145
Question: Let $ f(x)=x{{(-1)}^{[1/x]}},x\ne 0, $ where [x] denotes the greatest integer less than or equal to x then, $ \underset{x\to 0}{\mathop{\lim }}f(x)= $
Options:
A) Does not exist
2
0
-1
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \because [1/x]=integer $
$ \therefore {{(-1)}^{[1/x]}}=1 \text{ or } -1 $
$ \underset{x\to 0}{\mathop{\lim }}x{{(-1)}^{[1/x]}}=\underset{h\to 0}{\mathop{\lim }}h\cdot (-1)^{[1/h]} $
$ =\underset{h\to 0}{\mathop{\lim }}(-h)(1\text{ or }-1)=0 $
BETA
