1.

Let f(x)=`{{:(,(tanx-cotx)/(x-(pi)/(4)),x ne (pi)/(4)),(,a,x=(pi)/(4)):}` The value of a so that f(x) is a continous at `x=pi//4` is.A. 2B. 4C. 3D. 1

Answer» Correct Answer - B
If f(x) is continous at `x=(pi)/(4)`, then
`f((pi)/(4))=underset(x to pi//4)lim f(x)`
`Rightarrow a=underset(x to pi//4)lim (tan x- cotx )/(x-(pi)/(4))`
`Rightarrow a=underset(x to pi//4)lim (sin^(2)x-cos^(2)x)/((x-(pi)/(4))sin x cos x)`
`Rightarrow a=underset(x to pi//4)lim (sin2((pi)/(4)-x))/(2((pi)/(4)-x))xx(1)/(sinx cos x)`
`Rightarrow a=2xx1xx2=4`


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