Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Evaluate lim x tends to 0 f x , where f x=mode x/x for x not equal to 0

25. Evaluate \lim_{x \rightarrow 0} f (x) , \: \: where \: \: f (x) = \left\{\begin{matrix} \frac{|x|}{x} & x \neq 0 \\ 0 & x = 0 \end{matrix}\right.

Answers (1)

best_answer

\lim_{x \rightarrow 0} f (x) , \: \: where \: \: f (x) = \left\{\begin{matrix} \frac{|x|}{x} & x \neq 0 \\ 0 & x = 0 \end{matrix}\right.

The right-hand Limit or  Limit at x=0^+

\lim_{x \rightarrow 0^+} f (x) = \lim_{x \rightarrow 0^+} \frac{|x|}{x}=\frac{x}{x}=1

The left-hand limit or Limit at x=0^-

\lim_{x \rightarrow 0^-} f (x) = \lim_{x \rightarrow 0^-} \frac{|x|}{x}=\frac{-x}{x}=-1

Since Left-hand limit and right-hand limit are not equal, The limit of this function at x = 0 does not exists.

Posted by

Pankaj Sanodiya

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE 12th Computer Science Analysis 2026: Competency-based, direct questions, ‘easy’ MCQs; IP paper ‘balanced’
anam-khan

CBSE Class 12 Computer Science, IT, IP Exam 2026 LIVE: Question papers 'moderate', analysis updates
anam-khan

CBSE Board 12th Exams 2026 LIVE: Class 12 political science exam 'moderate' in difficulty; simple MCQs

Latest Question