Test Index

NCERT Class XI Mathematics - Limits and Derivatives - Solutions

© examsnet.com
Question : 24
Total: 72
Find
lim
x→1
 f (x) , where f (x) = {
x2−1x≤1
−x2−1x>1
Solution:  
We have, f (x) = {
x2−1x≤1
−x2−1x>1
Now,
lim
x→1
 f (x) =
lim
x→1
 (x2−1) = 12 - 1 = 0.
and
lim
x→1+
 f (x) =
lim
x→1+
 (−x2−1) = −(1)2 - 1
= - 1 - 1 = - 2.
Since
lim
x→1−
 f (x) ≠
lim
x→1+
 f (x)
∴
lim
x→1
 f (x) does not exist.
© examsnet.com
Go to Question:
Prev Question
Next Question