If `f` and `g` are differentiable at `a in R` such that `f(a) = g(a) = 0` and `g'(a) != 0` then show that `lim_(x -> a) f(x) / g(x) = (f'(a)) / (g'(a))`

If f (a) = 2 , f'(a) = 1, g (a) = -1 and g'(a) = 2 , show that lim_(x to a)(g(x)f(a)-f(x)g(a))/(x-a) = 5

f and g differentiable functions of x such that f(g(x))=x," If "g'(a)ne0" and "g(a)=b," then "f'(b)=

If f and g are derivable function of x such that g'(a)ne0,g(a)=b" and "f(g(x))=x," then 'f'(b)=

Let f and g be differentiable on R and suppose f(0)=g(0) and f'(x) =0. Then show that f(x) =0

If f(x) and g(x) are differentiable function for 0 le x le 23 such that f(0) =2, g(0) =0 ,f(23) =22 g (23) =10. Then show that f'(x)=2g'(x) for at least one x in the interval (0,23)

If f and g are continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

If f(a) = 2, f'(a) = 1, g(a) = -1 and g'(a) = 2 , find the value of lim_(x rarr a)(g(x)f(a) - g(a)f(x))/(x-a)

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

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