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-3 ∞ *DNE? -∞ *DNE? DNE Undefined undefined -2 3 DNE 3 0

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2.2 (CONT) Limits: numerically Graphically estimate the limit of: Graphically estimate the limit of:  Estimate the limit using a table of values.

Limits: numerically Graphically estimate the limit of: Graphically estimate the limit of:  Estimate the limit using a table of values.

Limits: numerically Graphically estimate the limit of: Graphically estimate the limit of:  Estimate the limit using a table of values.

Example (cont’d)

Limits: numerically Graphically estimate the limit of: Graphically estimate the limit of:  Estimate the limit using a table of values.

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Section 2.3 Calculating Limits Algebraically SWBAT SWBAT –Calculate limits using limit laws

Direct Substitution Property Let’s start with the following: Let’s start with the following: If you can evaluate the limit at a, then do it. If you can evaluate the limit at a, then do it. This is also known as “Plug and Chug” This is also known as “Plug and Chug”

If you cant “plug and chug”, Try something algebraic. Find Find

Solution Here is a general principle: Here is a general principle:

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Review Using the Limit Laws to calculate limits Using the Limit Laws to calculate limits Additional Properties of Limits Additional Properties of Limits Direct Substitution Property Direct Substitution Property

Assignment 6 p , 9-23 odd p , 9-23 odd

Lets look at : Lets look at : You must do some algebra or trig. To simplify first:You must do some algebra or trig. To simplify first: What happens when you evaluate this next function? What happens when you evaluate this next function? You get what is called an Indeterminate form You get what is called an Indeterminate form (it can not be determined) like 0 / 0 (it can not be determined) like 0 / 0 Now plug and chug!:Now plug and chug!: The limit is 3The limit is 3

The Limit Laws (don’t write this down)

Further Limit Properties (if you think it would help you, then writ it down, if not they are on p. 109) Applying the Product Law repeatedly with g(x) = f(x) gives the following Power Law: Applying the Product Law repeatedly with g(x) = f(x) gives the following Power Law: Here are two obvious but useful limits: Here are two obvious but useful limits:

Further Properties (cont’d)

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