Let `g:R rarr R` be a differentiable function satisfying `g(x)=int_(0)^(x)(g(t)*cos t-cos(t-x))` for all `x in R` .Find number of integers in the range of `g(x)`

Let g:R rarr R be a differentiable function satisfying g(x)=int_(0)^(x)(g(t)*cos t-cos(t-x))dt for all x in R Find number of integers in the range of g(x)

Let f(x) be a derivable function satisfying f(x)=int_(0)^(x)e^(t)sin(x-t)dt and g(x)=f'(x)-f(x) Then the possible integers in the range of g(x) is

Let g:R rarr R be a differentiable function satisfying g(x)=g(y)g(x-y)AA x,y in R and g'(0)=a and g'(3)=b. Then find the value of g'(-3)

Let f:(0,oo)rarr(0,oo) be a differentiable function satisfying,x int_(x)^(x)(1-t)f(t)dt=int_(0)^(x)tf(t)dtx in R^(+) and f(1)=1 Determine f(x)

Let f:R to R and g:R to R be differentiable functions such that f(x)=x^(3)+3x+2, g(f(x))=x"for all "x in R , Then, g'(2)=

Let g (x) be a differentiable function satisfying (d)/(dx){g(x)}=g(x) and g (0)=1 , then g(x)((2-sin2x)/(1-cos2x))dx is equal to

A differentiable function y=g(x) satisfies int_(0)^(x)(x-t+1)g(t)dt=x^(4)+x^(2) for all x>=0 then y=g(x) satisfies the differential equation

Let f:R rarr R be a differentiable function such that f(0)=0,f(((pi)/(2)))=3 and f'(0)=1 If g(x)=int_(x)^((pi)/(2))[f'(t)cos ect-cot t cos ectf(t)]dt for x in(0,(pi)/(2)] then lim_(x rarr0)g(x)=