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

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

3. 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

4. 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

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

6. Evaluating Limits Analytically

7. 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?

8. 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

9. 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