Find `lim_(h->0) (h^2+2)/(h)`

If f'(3)=2 , then lim_(h->0)(f(3+h^2)-f(3-h^2))/(2h^2) is

Suppose f (x) is differentiable at x=1 and lim _(h to0) (f(1+h))/(h) =5. Then f '(1) is equal to-

lim_(h->0) (f(2h+2+h^2)-f(2))/(f(h-h^2+1)-f(1)) given that f'(2)=6 and f'(1)=4 then (a) limit does not exist (b) is equal to - 3/2 (c) is equal to 3/2 (d) is equal to 3

Suppose f(x) is differentibale for all x and lim_(h to 0) (1)/(h) (1+h)=5"then f'(1) equals"

f(x) is the integral of (2sinx-sin2x)/(x^3),x!=0. Find lim_(x->0)f^(prime)(x)[w h e r ef^(prime)(x)=(df)/(dx)]

Let f(x)=3x^10-7x^8+5x^6-21x^3+3x^2-7 , then the value of lim_(h->0) (f(1-h)-f(1))/(h^3+3h)

Evaluate: ("lim")_(h->0)((a+h)^2sin(a+h)-a^2sina)/h

If Delta=|{:(sinx,sin(x+h),sin(x+2h)),(sin(x+2h),sinx,sin(x+h)),(sin(x+h),sin(x+2h),sinx):}| find lim_(hto0)((Delta)/(h^(2))) .

Evaluate lim_(hto0) [(1)/(h^(3)sqrt(8+h))-(1)/(2h)].

Evaluate the limit: ("lim")_(h->0)[1/(8+h)^(1/3)-1/(2h)]