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## PowerPoint Slideshow about ' 1.5 Infinite limits' - reed-christian

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### 1.5 Infinite limits

"I never got a pass mark in math ... Just imagine -- mathematicians now use my prints to illustrate their books." -- M.C. Escher

Objective:

- To describe infinite limits

Black holes

- Start with any number
- Count the number of even digits, the number of odd digits, the total number of digits.
- Write that 3-digit number
- Repeat
- Repeat
- Repeat

Ways limits DNE

- Limit from the left is different than the limit from the right
- Function increases or decreases without bound
- Function oscillates

Function increases or decreases without bound

- If both the left and the right side approach infinity then
- If both the left and the right side approach negative infinity then

Discontinuities

- 2 types:
- Removable
- Non-removable

Def. of a vertical asymptote

- If f(x) approaches infinity or negative infinity as x approaches c from the right or left then the line x = c is a v. a. of the graph

V. A. theorem

- The functions f and g are continuous on an open interval. If f(c) does not equal zero, g(c) = 0, and g(x) is not zero for all other x in the interval then
has a v. a. at x = c

In other words

- Look for zeros in the denominator and then check the numerator to see if it is a hole or an asymptote

Limits and V. A.

- Find:
- What do you know about the function?

Cont..

- Check from the left:
- Check from the right:
- The limit is…

Properties of limits

- 1. Sum or difference:
- 2. Product:

More properties

- 3. Quotient
- These are also true for negative infinity

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