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

If f(x) is derivable at x=3 and f'(3)=2 , then value of lim_(hto0)(f(3+h^(2))-f(3-h^(2)))/(2h^(2)) is less than

If f ' (3)=1 , then Lt_(h to0)(f(3+h)-f(3-h))/(h) is

If f(x) is derivable at x=5, f'(5)=4 , then evaluate lim_(hto0)(f(5+h^(3))-f(5-h^(3)))/(2h^(3)

If f^(prime)(a)=1/4, t h e n(lim)_(hvec0)(f(a+2h^2)-f(a-2h^2))/(f(a+h^3-h^2)-f(a-h^3+h^2))= 0 b. 1 c. -2 d. none of these

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)

If f(x)= x^2 , then (f(x+h)-f(x))/(h) =

The value of lim_(hto0) (In (1+2h)-2ln (1+h))/(h^2) , is

If f(x) is derivable at x=2 such that f(2)=2 and f'(2)=4 , then the value of lim_(h rarr0)(1)/(h^(2))(ln f(2+h^(2))-ln f(2-h^(2))) is equal to

Instead of the usual definition of derivative Df(x), if we define a new kind of derivative D^*F(x) by the formula D*f(x)=lim_(h->0)(f^2(x+h)-f^2(x))/h ,w h e r ef^2(x) mean [f(x)]^2 and if f(x)=xlogx ,then D^*f(x)|_(x=e) has the value (A)e (B) 2e (c) 4e (d) none of these

Prove that lim_(x->0) (f(x+h)+f(x-h)-2f(x))/h^2 = f''(x) (without using L' Hospital srule).