Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Evaluate the following limits limit z tends to 1 z^ 1 / 3 - 1

10.   Evaluate the following limits \lim_{z\rightarrow 1} \frac{z^{1/3}-1}{z^{1/6}-1}

Answers (1)

best_answer

The limit

\lim_{z\rightarrow 1} \frac{z^{1/3}-1}{z^{1/6}-1}

Here on directly putting limit , both numerator and the denominator becomes zero so we factorize the function and then put the limit.

\lim_{z\rightarrow 1} \frac{z^{1/3}-1}{z^{1/6}-1}=\lim_{z\rightarrow 1} \frac{z^{(1/6)^2}-1^2}{z^{1/6}-1}

=\lim_{z\rightarrow 1} \frac{(z^{(1/6)}-1)(z^{(1/6)}+1)}{z^{1/6}-1}

=\lim_{z\rightarrow 1} (z^{(1/6)}+1)}

= (1)(1/6) + 1

=1+1

=2  (Answer)

 

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 Date Sheet 2025 (Out) Live: Class 10, 12 board exam time table at cbse.gov.in; syllabus, sample papers
anam-khan

CBSE Class 12 board exam date sheet 2025 out; exams from February 15 to April 4
anam-khan

When will CBSE Board exam 2025 date sheet be released for Class 10, 12?

Latest Question