If `f(x)={sin((a-x)/2)t a n[(pix)/(2a)]` for `x > a` and
`([cos((pix)/(2a))])/(a-x)` for `x < a,` then `a. f(a^-)<0` b. `f` has a removable discontinuity at `x=a` c. `f` has an irremovable discontinuity at `x=a` d. `f(a^+)<0`

lim_(x to 1) (1-x)tan((pix)/2)

If f'(x)=(sin2x)/(cos^(2)2x)," then "f(x) =

Period of the function f(x)=sin((x)/(2))cos [(x)/(2)]-cos((x)/(2))sin[(x)/(2)] , where [.] denotes the greatest integer function, is _________.

Evaluate: lim_(xto(1)/(2))(sin((pix)/(2))-cos((pix)/(2)))/((1)/(2)-x)

If f(a)=lim_(xto2)(sin^(x)a+cos^(x)a)^((1)/((x-2)))" for "ain[0,(pi)/(2)], then f(a)=?

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Which of the following is true?

Find the period of f(x)=sin((pix)/(n !))-cos((pix)/((n+1)!))

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Consider the statements : P : there exists some x in RR such that f(x)+2x=2(1+x^(2)) Q : There exists some x in RR such that 2f(x)+1=2x(1+x) then-

Let f(x)=sin^(4)x-cos^(4)x int_(0)^((pi)/(2))f(x)dx =

Let f(x)=sin^(4)x-cos^(4)xandg(x)=1-2sin^(2)xcos^(2)x . int_(0)^((pi)/(4))(f(x))/(g(x))dx =