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Question

If the function f(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪[tan(π4+x)]1x,for x0K,x=0

is continuous at x=0, then K=?

A
e
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B
e1
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C
e2
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D
e2
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Solution

The correct option is C e2
Given : f(x) is continuous at x=0
f(0)=limx0f(x)
=limx0[tan(π4+x)]1x
=limx0(1+tanx1tanx)1x
=limx0(1+tanx)1tanxtanxx(1tanx)1tanxtanxx
taking limits
=e1e1=e1.e1=e2

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