1. The problem statement, all variables and given/known data Given y = sin x + cos x , evaluate limit h approaches 0 of [(f(pi+h)-f(pi)]/h 2. Relevant equations d/dx (sin x) = cos x d/dx (cos x) = -sin x 3. The attempt at a solution This was a question on my quiz today. Its answer, which I knew from the glance, had to be the derivative of the equation at x = pi. Using d/dx rule, dy/dx = cos x - sin x at x = pi; cos pi - sin pi = -1 - 0 = -1 I found the answer by using derivative rules but I couldn't do it using the limit concept. lim h->0 [(sin pi+h)+(cos pi+h)-(sin pi)-(cos pi)]/h lim h->0 [(sin pi)(cos h)+(cos pi)(sin h)+(cos pi)(cos h)-(sin pi)(sin h)-(sin pi)-(cos pi)]/h lim h->0 [0-(sin h)-(cos h)-0-0+1]/h lim h->0 [1-(sin h)-(cos h)]/h That's as far as I've got. I couldn't cancel the h in the denominator. Please help, thank you.