If `f(x)=x^2+4`, `t=z-1` then find `f(t)`

If f(x)=3-2x+x^(2) , then ((f(x+t)-f(x))/(t)) =

If f(x) = int_(x)^(x^(2)) t^(2)lnt then find f'(e)

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

If lim_(trarrx)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2), then find the value of f'(0).

If lim_(trarrx) (e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2), then find the value of f'(0).

If f(x)=t^(2)+(3)/(2)t , then f(q-1)=

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

If f(x) is a function such that f(x-1)+f(x+1)=sqrt3t(x) and f(5)=100 , then find sum_(t=0)^(19)f(5+12r) .

If y=1/(t^2+t-2),where \ t=1/(x-1), then find the number of points where f(x) is discontinuous.