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