Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let a1, a2, . . ., an be fixed real numbers and define a function f x = (x - a1 ) (x - a2 )...(x - an ) . What is 1 limit x tends to a f (x) ? For some a not equal to a1, a2, ..., an, compute limit x tends to a f (x).

29. Let a1, a2, . . ., an be fixed real numbers and define a function f (x) = (x - a_1 ) (x - a_2 )...(x - a_n ) . What is  \lim_{x \rightarrow a _ 1 }  f (x) ? For some a \neq a _ 1 , a _ 2 .... a _n , compute l\lim_{ x \rightarrow a } f (x)

Answers (1)

best_answer

Given,

f (x) = (x - a_1 ) (x - a_2 )...(x - a_n ) .

Now,

\\\lim_{x \rightarrow a _ 1 }f(x)=\lim_{x \rightarrow a _ 1 }[(x - a_1 ) (x - a_2 )...(x - a_n ) ]\\.=[\lim_{x \rightarrow a _ 1 }(x - a_1 )][\lim_{x \rightarrow a _ 1 }(x - a_2 )][\lim_{x \rightarrow a _ 1 }(x - a_n )] \\=0

Hence

, \lim_{x \rightarrow a _ 1 }f(x)=0

Now,

\lim_{ x \rightarrow a } f (x)=\lim_{ x \rightarrow a } (x-a_1)(x-a_2)...(x-a_n)

\lim_{ x \rightarrow a } f (x)=(a-a_1)(a-a_2)(a-a_3)

Hence 

\lim_{ x \rightarrow a } f (x)=(a-a_1)(a-a_2)(a-a_3).

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 Results 2024: Last 9 years’ CBSE Class 10, 12 result date and time; links to check score
anam-khan

CBSE Board exams twice a year from 2025, no plan for semesters: MoE
anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th

Latest Question