Let `f(x) =int_(-2)^xe^((1+t)^2)dt` and `g(x) = f(h(x))`,where h(x) is defined for all `x in R`. If `g'(2) = e^4` and `h' (2)=1` then absolute value of sum of all possible values of h(2), is

Let f(x) =int_-1^x e^(t^2) dt and h(x)=f(1+g(x)), where g (x) is defined for all x, g'(x) exists for all x, and g(x) 0. If h'(1)=e and g'(1)= 1, then the possible values which g(1) can take

Let f(x) =int_-1^x e^(t^2) dt and h(x)=f(1+g(x)), where g (x) is defined for all x, g'(x) exists for all x, and g(x) 0. If h'(1)=e and g'(1)= 1, then the possible values which g(1) can take

Let f(x)=int_(-1)^(x)e^(t^(2))dt and h(x)=f(1+g(x)) where g(x) is defined for all x,g'(x) exists for all,x, and g(x) 0. If h'(1)=e and g'(1)=1, then the possible values which g(1) can take

Let f(x)=int_(2)^(x)(dt)/(sqrt(1+t^(4))) and g be the inverse of f. Then,the value of g'(x) is

Let f(x) = e^(x) - x and g (x) = x^(2) - x, AA x in R . Then the set of all x in R where the function h(x) = (f o g) (x) in increasing is :

let f(x)=e^x ,g(x)=sin^(- 1) x and h(x)=f(g(x)) t h e n f i n d (h^(prime)(x))/(h(x))

Let f(x)=(2x+7)/(9) and g(x)=(9x+5)/(7) and we define h(x)=f^(-1)(x)+g^(-1)(x)-5x . If (h^(-1)(x)=(ax+b)/(c)) where c is a prime then the value of 5a-2c-b is equal to

Let f: R rarr R be a continuous odd function, which vanishes exactly at one point and f(1)=1/2 . Suppose that F(x)=int_(-1)^xf(t)dt for all x in [-1,2] and G(x)=int_(-1)^x t|f(f(t))|dt for all x in [-1,2] . If lim_(x rarr 1)(F(x))/(G(x))=1/(14) , Then the value of f(1/2) is