If f(a) exists, prove, that `lim_(hrarr0)(f(a+h)-f(a-h))/(2h)=f'(a)`

If f(x) is derivable at x = a,show that lim_(xrarra)(xf(a)-af(x))/(x-a)=f(a)-af'(a)

Prove that F = ma.

If f(x) is derivable at x = h,show that lim_(xrarrh)((x+h)f(x)-2hf(h))/(x-h)=f(h)+2hf'(h)

If f (2) = 4 andf'(2) = 1, show that lim_(xrarr2)(xf(2)-2f(x))/(x-2)=2

If y= |(f(x),g(x),h(x)),(l,m,n),(a,b,c)| ,prove that (dy)/(dx)=|(f'(x),g'(x),h'(x)),(l,m,n),(a,b,c)| .

If f(x)=x|x| , then find f'(0).

If f(x)=xcos x + e^(x) , then find f'(0) .

if lim_(xrarra)f(x)=l , lim_(xrarra)g(x)=m lim_(xrarra)h(x)=n ,find the values of lim_(xrarra){f(x)g(x)h(x)}

If f(x)=ax^2+bx+c find a, b, c given that f(1)= 4,f(2)=13,f(-2)=1.