If f(x)=|x+2|tan −1⁡(x+2), x≠−22, x=-2then f(x) is

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Continuous at x=−2

not continuous at x=−2

Differentiable at x=−2

continuous but not differentiable at x=−2

answer is B.

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Detailed Solution

limx→−2−f(x)=limx→−2−x+2tan−1x+2=limx→−2−−x+2tan−1x+2=−1 ∵limx→0−tan−1xx=1limx→−2+f(x)=limx→−2+x+2tan−1x+2=limx→−2+x+2tan−1x+2=1∴limx→−2f(x) does not exist.

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