1. AP Calculus BC
September 28, 2016

2. Entry Task
Prove that the following limits are true three different ways:
lim 𝒙→∞ 𝟑 𝒙 𝟐 𝒙 𝟐 +𝟏 =𝟑
lim 𝒙→−∞ 𝟑 𝒙 𝟐 𝒙 𝟐 +𝟏 =𝟑
Ratio, dividing by x^2, calculator

3. Learning Targets I can analyze and sketch the graphs of functions.
I used intercepts, asymptotes, domain/range, extrema, concavity, points of inflection, and limits to analyze and sketch graphs of functions.

4. Sketching Curves Tools to help in curve sketching: x- and y-intercepts
Symmetry
Domain and Range
Continuity and Differentiability
Vertical and Horizontal Asymptotes
Relative Extrema
Concavity
Points of Inflection

5. Analyze and sketch the graph of 𝒇 𝒙 = 𝟐( 𝒙 𝟐 −𝟗) 𝒙 𝟐 −𝟒

6. Analyze and sketch the graph of
𝒇 𝒙 = 𝒙 𝒙 𝟐 +𝟐

7. Assignment #13
Page : 17, 19, 27, 33, 36, 37, 40, 47,