Given the following definitions:
The differential of x, denoted by dx, is defined by: dx = delta x
The differential of y, denoted by dy, us defined by: dy = f'(x)dx
For the curve f(x) = sin(x) between x = pi/6 and x = pi/4, find the exact values of:
1) The point P1 on the curve at x = pi/6
2) The point P2 on the curve at x = pi/4
3) f'(pi/6)
4) The equation of the tangent at P1: x = pi/6
5) The point P3 on the tangent when x = pi/4
6) dx
7) dy
8) delta y between P1 and P2 (note that dy > delta y)
9) the ratio, dy (from 7) divided by dx (from 6) and compare to (3)
A picture is worth a thousand words. Cheers - Ian