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L e t f(x)=(1-tanx)/(4x-pi),x!=pi/4,x in...

`L e t` `f(x)=(1-tanx)/(4x-pi),x!=pi/4,x in [0,pi/2],` If`f(x)i s` continuous in `[0,pi/4],` then find the value of `f(pi/4)dot`

A

1

B

`1//2`

C

`-1//2`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
Since, `f(x)=(1-tanx)/(4x-pi)`
Now, `lim_(x to pi//4) f(x)=lim_(x to pi//4) ((1-tan x)/(4x-pi))`
`=lim_(x to pi//4)((-sec^(2)x)/(4))=-(1)/(2)`
Since, f(x) is continuous at `x=(pi)/(4).`
`lim_(x to pi//4)f(x)=f((pi)/(4))=-(1)/(2)`
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