Differentiation Question 467
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\text{ or }-1)=0 $ $ =\underset{h\to 0}{\mathop{\lim }},(-h)\cdot(1\text{ or }-1)=0 $
BETA
