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Question

Question: \[\lim_{x \rightarrow 0}\frac{|x|}{x} =\]...

lim⁡x→0∣x∣x=\lim_{x \rightarrow 0}\frac{|x|}{x} =

A

1

B

–1

C

0

D

Does not exist

Answer

Does not exist

Explanation

Solution

∵lim⁡x→0−∣x∣x=−1\because\lim_{x \rightarrow 0 -}\frac{|x|}{x} = - 1 andlim⁡x→0+∣x∣x=1\lim_{x \rightarrow 0 +}\frac{|x|}{x} = 1,

hence limit does not exists.