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Question

The value of limx1(4πtan1x)1x21 is equal to


Your Answer
A
1π
Your Answer
B
1π 
Correct Answer
C
e1/π
Your Answer
D
e1/π 

Solution

The correct option is C e1/π
limx1(4πtan1x)1x21=e limx1(4πtan1x1)x21=eL

Now,
L=limx1(4πtan1x1)x21
Using L'Hospital's rule,
L=limx1(4π(1+x2))2xL=44π=1π
Therefore,
limx1(4πtan1x)1x21=e1/π

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