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Question

If f(x)=|x+2|tan1(x+2),x22,x=2, then f(x) is

A
Continuous at x=2
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B
Not continuous at x=2
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C
Differentiable at x=2
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D
Continuous but not derivable at x=2
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Solution

The correct option is A Not continuous at x=2
Given, f(x)=|x+2|tan1(x+2),x22,x=2
limx2f(x)=limh0f(2h)
=limh0|2h+2|(2h+2)
=limh0htan1h=1
and limx2+f(x)=limh0f(2+h)
=limh0[|2+h+2|tan1(2+h+2)]
=limh0htan1h=1
limx2f(x)limx2+f(x)
So, f(x) is not continuous as well as not differentiable at x=2.

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