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:
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