Question:
If
f(x)=
begincases
(xlog(cos x))/(log(1+x²)), & x\ne0
0, & x=0
endcases
then f(x) is
If
f(x)=
begincases
(xlog(cos x))/(log(1+x²)), & x\ne0
0, & x=0 endcases then f(x) is
0, & x=0 endcases then f(x) is
Show Hint
Continuity does not always guarantee differentiability.
Updated On: Mar 20, 2026
- continuous as well as differentiable at x=0
- continuous but not differentiable at x=0
- differentiable but not continuous at x=0
- neither continuous nor differentiable at x=0
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The Correct Option is B
Solution and Explanation
Step 1: Using limits: limₓ\to0f(x)=0 ⟹ continuous
Step 2: Derivative limit fails to exist.
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