Calculus
posted by Marissa on .
Assuming that f and g are functions differentiable at a (though we do not know their formulas). Prove that f +g is differentiable at a using the definition of the derivative.

we know these limits exist as h>0:
(f(a+h)f(a))/h
(g(a+h)g(a))/h
sum of limits is thus
(f(a+h)f(a) + g(a+h)g(a))/h
= (f(a+h)+g(a+h)  (f(a)+g(a))/h
= ((f+g)(a+h)  (f+g)(a))/h
the limit is d(f+g)/dx at x=a