If `f''(x)=f( x)` where, f(x) is a continuous double differentiable function and `g(x)= f'(x)`. If `F(5)=5`, then `F(10)` is equal to

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuous differentiable function with f'(x) !=0 and satisfies f(0)=1 and f'(0)=2 , then f(x)=e^(lambda x)+k , then lambda+k is equal to ..........

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuous differentiable function with f'(x) !=0 and satisfies f(0)=1 and f'(0)=2 , then f(x)=e^(lambda x)+k , then lambda+k is equal to ..........

Let f(x) be a continuous & differentiable function on R satisfying f(-x)=f(x)&f(3+x)=f(3-x)AA x in R . If f'(1)=-5 then f'(7) =

If f is continuously differentiable function then int_(0)^(2.5) [x^2] f'(x) dx is equal to

If g is the inverse function of f an f'(x)=(x^(5))/(1+x^(4)). If g(2)=a, then f'(2) is equal to

If f(x) is a twice differentiable function such that f'' (x) =-f,f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) is equal to

Let f be the continuous and differentiable function such that f(x)=f(2-x), forall x in R and g(x)=f(1+x), then

If f(x) is a twice differentiable function such that f'' (x) =-f(x),f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) is equal to