Q.
If fx=xlog cosxlog1+x2, x≠00, x=0, then
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a
f(x) is not continuous at x = 0
b
f(x) is continuous at x = 0
c
f(x) is continuous at x = 0 but not differentiable at x = 0
d
f(x) is differentiable at x = 0
answer is B.
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Detailed Solution
We have limx→0 fx-f0x-0= limx→0 log cosxlog1+x2 =limx→0log1-1+cosxlog1+x21-cosx1-cosx =limx→0log1-1-cosx1-cosx1-cosxlog1+x2 =limx→0 log1-1-cosx11-cosx2sin2x24x2x2log1+x2=-12Hence, fx is differetiable x=0.Hence, (2') and (4) are the correct answers.
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