If `f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R ` be differentiable function and `f(g(x))` is differentiable at `x=a`, then

If f(x)a n dg(f) are two differentiable functions and g(x)!=0 , then show trht (f(x))/(g(x)) is also differentiable d/(dx){(f(x))/(g(x))}=(g(x)d/x{f(x)}-g(x)d/x{g(x)})/([g(x)]^2)

Let f : R to R be differentiable at c in R and f(c ) = 0 . If g(x) = |f(x) |, then at x = c, g is

If f(x)a n dg(x) are two differentiable functions, show that f(x)g(x) is also differentiable such that d/(dx)[f(x)g(x)]=f(x)d/(dx){g(x)}+g(x)d/(dx){f(x)}

If f(-x)+f(x)=0 then int_a^x f(t) dt is

f(x) is differentiable function and (f(x).g(x)) is differentiable at x = a . Then (a) g(x) must be differentiable at x=a (b.) if g(x) is discontinuous, then f(a)=0 (c.) if f(a)!=0 , then g(x) must be differentiable (d.) none of these

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and STATEMENT 2 : g(x)=f'(x) is an even function , then f(x) is an odd function.

If f(x)a n dg(x) a re differentiate functions, then show that f(x)+-g(x) are also differentiable such that d/(dx){f(x)+-g(x)}=d/(dx){f(x)}+-d/(dx){g(x)}

Let f : R to R be a differentiable function and f(1) = 4 . Then, the value of lim_(x to 1)int_(4)^(f(x))(2t)/(x-1)dt is :

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2 and f(1)=1, then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then