Evaluating Limits Analytically Day 2 Evaluating Limits Analytically AP Calculus BC Mr. Chopyak

Entry Task Evaluate the limit lim 𝒙→𝟑 (𝒙 𝟐 +𝟒) graphically and numerically.

Learning Targets I evaluate limits analytically using properties of limits and analysis techniques. I correctly evaluated limits for: Polynomial functions Rational functions Radical functions Trigonometric functions

Review Section 1.2 Definition of a Limit: If f(x) becomes arbitrarily close to a single number L as x approaches c from either side, then the limit of f(x), as x approaches c, is L, or: lim 𝒙→𝒄 𝒇(𝒙) =𝐋

Review Section 1.2 Limits don’t exist when: Behavior is different from the right and left Behavior is unbounded Oscillating behavior

Evaluating Limits Analytically

Exit Ticket lim 𝒙→𝟐 𝟐 𝒙 𝟐 −𝟑𝒙+𝟏 𝟐 𝒙 𝟑 −𝟐𝟓 is (A)− 𝟏 𝟑 (B) − 𝟏 𝟐𝟓 (C) 1 (D) 2 Which of the following limits do not exist? (A)None (B) I and II only (C) III only (D) I,II,III lim 𝒙→𝟑 𝒙 𝟒 −𝟖𝟏 𝒙−𝟑 is?

Learning Targets I evaluate limits analytically using properties of limits and analysis techniques. I correctly evaluated limits for: Polynomial functions Rational functions Radical functions Trigonometric functions

Assignment #2 Due tomorrow Do §1.3 #39, 46, 53, 55, 59, 65, 74, 117, 120 Due by September 9 (next Friday) Show me your signed syllabus page