AP Calculus BC September 28, 2016

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

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.

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

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

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

Assignment #13 Page 205-208: 17, 19, 27, 33, 36, 37, 40, 47, 107-108