# AB2.3 - Calculating Limits Using the Limit Laws

 0

Slide 1

Section 2.3 Calculating Limits Using the Limit Laws "It is our choices, Harry, that show what we truly are, far more than our abilities." - Albus Dumbledore

Slide 2

(The limit of a sum is the sum of the limits.) (The limit of a difference is the difference of the limits.) The limit of a constant times a function is the constant times the limit of a function. The limit of a product is the product of the limits. The limit of a quotient is the quotient of the limits (provided that the limit of the denominator is not 0).

Slide 3

where n is a positive integer where n is a positive integer where n is a positive integer where n is a positive integer (If n is even, we assume that a>0.) (If n is even, we assume that

Slide 4

Direct Substitution Property: If f is a polynomial or a rational function and a is in the domain of f, then:

Slide 5

Example 1

Slide 6

Example 2 Evaluate the following limits and justify each step:

Slide 7

Example 3 Find

Slide 8

If when , then , provided the limits exist.

Slide 9

Example 4 Find Where

Slide 10

Example 5 Evaluate

Slide 11

Example 6 (the trick!)

Slide 12

Theorem: If and only if And

Slide 13

Example 7 Show that

Slide 14

Example 8: Prove that does not exist.

Slide 15

Example 9 If Determine whether Exists.

Slide 16

Example 10 the largest integer that is less than or equal to x. (For instance, The greatest integer function is defined by Show that does not exist.

 URL:
More by this User
Most Viewed