Reflection

This week was our holiday, so I'll do a blog to review some of the stuff we learned throughout the year. We have learned information from chapters 1, 2, 3, and 5, but out of all of them, I think 3 was the most difficult.

2.5 Implicit Derivatives
When solving for implicit derivatives, it is easiest to solve by following 5 steps.
Steps:
1) Differentiate both sides with respect to x. d_/dx
2) Collect all dy/dx terms on one side, and move the other terms to the other side.
3) Factor out dy/dx.
4) Solve for dy/dx.
5) Simplify.
EXAMPLE:
x^2 + y^2 = 0
2x + 2ydy/dx = 0
2ydy/dx = -2x
dy/dx = -2x/2y
= -x/y

Chapter 1
EXAMPLES:
1) lim tanx/x = sinx/cosx/x/1
x>0
= (sinx/x)(1/cosx)
= (1)(1/cos(0))
= (1)(1)
= 1

2) h(x) = -x^2 + 4x
a) lim h(x) = -(4)^2 + 4(4) = 32
x>4
b) lim h(x) = -(-1)^2 + 4(-1) = 5
x>-1