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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

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1 5 infinite limits

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
Objective:

  • To describe infinite limits


Black holes
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
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
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
Discontinuities

  • 2 types:

  • Removable

  • Non-removable


Def of a vertical asymptote
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
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
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
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
Properties of limits

  • 1. Sum or difference:

  • 2. Product:


More properties
More properties

  • 3. Quotient

  • These are also true for negative infinity



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