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

If f(x)=x3+x216x+20(x2)2,x2

=k,x=2 is continuous at x=2, find the value of k.

Open in App
Solution

The given function is continuous at x=2.
Therefore,
limx2f(x)=limx2+f(x)=f(2)
limx2=f(2)
Now, consider limx2f(x)=limx2x3+x216x+20(x2)2

=limx2(x+5)(x2)2(x2)2

=limx2(x+5)=7
Therefore,
7=f(2)=k
Hence, the required value of k is 7.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Continuity of a Function
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon