CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let f(x)={x2sin1x,x00,x=0. Then

A
f does not exist at x=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
f exists and is continuous at x=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
f exists but not continuous at x=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
f does not exist at any point
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C f exists but not continuous at x=0
Clearly, f(x) exists for all x0

f(0)=limh0f(h)f(0)h=limh0h2sin1hh
=limh0hsin1h=0
f(0) exists and equals 0

When x0,
f(x)=cos1x+2xsin1x
limh0f(0) and limh0f(0+) do not exist.
Hence, f is not continuous at x=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Derivative of Simple Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon