Reflection #3 Terrio

This week we did chapter 1.5 (not sure on the name of this but it's something with limits) and chapter 2 (Derivatives).

-Degree of top=Degree of bottom: then limit is the coefficient

-Degree of top>Degree of bottom: then limit is infinity or negative infinity

-Degree of top
Example:

lim
x->infinity

Derivatives:

If the problem has dy/dx, y', d/dx, Dx[y], the slope of a tangent line, or the slope of a curve at a point then you solve for a derivative.

Formula for derivative: f(x+Δx-f(x)/Δx

Find dy/dx of x^2+1 at (0,1),(-1,2)

(x+Δx)^2+1-(x^2+1)/(Δx)
x^2+2xΔx+Δx^2+1-x^2-1/Δx
2xΔx+Δx^2/Δx
Δx(2x+Δx)/Δx
2x+Δx
=2x

Plug the two points in equation.
(0,1) slope=2(0)=0
(-1,2) slope=2(-1)=-2