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 x tends to 0 x + 1 ^ 5 -1/ x

6.   Evaluate the following limits \lim_{x \rightarrow 0 }\frac{( x+1)^5 -1}{x }

Answers (1)

best_answer

The limit 

\lim_{x \rightarrow 0 }\frac{( x+1)^5 -1}{x }

Lets put 

 x+1=y

since we have changed the function, its limit will also change,

so

x\rightarrow 0,y\rightarrow 0+1=1

So our function have became

\lim_{y \rightarrow 1 }\frac{ y^5 -1}{y-1 }

Now As we know the property 

\lim_{x \rightarrow 1 }\frac{ x^5 -a^n}{x-a }=na^{n-1}

 

\lim_{y \rightarrow 1 }\frac{ y^5 -1}{y-1 }=5(1)^5=5

Hence,

\lim_{x \rightarrow 0 }\frac{( x+1)^5 -1}{x }=5

 

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 Class 12 supplementary practical exams from July 29; check exam guidelines, rules
anam-khan

CBSE Class 12 supplementary admit card out; exam on July 28 for over 2.5 lakh
anam-khan

CBSE Class 12 supplementary exams 2026 datesheet out; test on July 28

Latest Question