KCET · Maths · Limits
The value of \( \lim _{x \rightarrow 0} \frac{[x]}{x} \) is
- A \( 1 \)
- B \( -1 \)
- C \( 0 \)
- D Does not exist
Answer & Solution
Correct Answer
(D) Does not exist
Step-by-step Solution
Detailed explanation
Given that \( \lim _{x \rightarrow 0} \frac{|x|}{x} \)
So, \( \lim _{x \rightarrow 0^{+}} \frac{|x|}{x}=1 \)
and \( \lim _{x \rightarrow 0^{-}} \frac{|x|}{x}=-1 \)
Therefore, limit does not exist
So, \( \lim _{x \rightarrow 0^{+}} \frac{|x|}{x}=1 \)
and \( \lim _{x \rightarrow 0^{-}} \frac{|x|}{x}=-1 \)
Therefore, limit does not exist
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