Question

If f(x)= begincases (xlog(cos x))/(log(1+x²)), & x≠0
0, & x=0 endcases then f(x) is

• A. continuous as well as differentiable at x=0
• B. continuous but not differentiable at x=0
• C. differentiable but not continuous at x=0
• D. neither continuous nor differentiable at x=0

Hint:

Continuity does not guarantee differentiability.

Answer 1

The Correct Option is B

Using limits: limₓ\to0f(x)=0=f(0) So, function is continuous. But derivative at 0 does not exist.