y = g(x) = cos(x)

Question

Can someone show how to estimate g'(pi/2) using the limit definition of the derivative and different values of h.

Thanks!

Answer 1

g'(x) ≈ ∆g/∆x = [g(x+h)-g(x)]/h
So, just pick a small h, and figure

[g(π/2 + h)-g(π/2)]/h
= [cos(π/2 + h)-cos(π/2)]/h
= [(cos(π/2)cos(h) - sin(π/2)sin(h)-cos(π/2)]/h
= -sin(h)/h

So, pick any value of h close to zero, and that approximates g'(π/2). g' is exactly the limit as h->0.

Answer 2

Thank You very much, I understand it now