First slide
Continuity
Question

Iffx=xlogcosxlog1+x2,x00,        x=0, then

Moderate
Solution

Wehavelimx0fx-f0x-0=limx0logcosxlog1+x2=limx0log1-1+cosxlog1+x21-cosx1-cosx=limx0log1-1-cosx1-cosx1-cosxlog1+x2=limx0log1-1-cosx11-cosx2sin2x24x2x2log1+x2=-12Hence,fxisdifferetiablex=0.

Hence, (2') and (4) are the correct answers.

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