SPC calc sec 1.5 infinite limits.notebook
Remember:
Vertical Asymptotes and Holes
Find all intercepts, asymptotes and/or holes. Then sketch a graph.
For each function below, analytically find the single real number c that is not in the domain.
Use your graphing calculator to graph each function and find each limit of f(x) as x approaches c
from the left and from the right.
Limits like these, where f(x) increases or decreases without bound
as x approaches c are called infinite limits.
**A word of caution**
Does NOT mean the limit exists!
It tells you how it fails to exist by explaining the unbounded behavior.
May 06, 2015
SPC calc sec 1.5 infinite limits.notebook
May 06, 2015
Properties of Infinite Limits Let c and L be real numbers and let f and g be functions such that
and
1. Sum or Difference:
2. Product:
3. Quotient:
Properties also hold for one sided limits and limits approaching -∞.
Evaluate the following limits.
Try some other values for
.
What is the
for all values of n?
SPC calc sec 1.5 infinite limits.notebook
Limits approaching infinity or negative infinity
If x is approaching infinity or negative infinity:
divide the numerator and the denominator
by the highest power of x in the denominator.
You will get several
terms which will go to 0 as x approaches infinity.
Evaluate each Limit.
May 06, 2015
SPC calc sec 1.5 infinite limits.notebook
Short cut...
Finding limits at infinity follow the same rules as horizontal asymptotes.
Find the limit:
Example: Determine the limit.
May 06, 2015
SPC calc sec 1.5 infinite limits.notebook
May 06, 2015
Homework:
Calculus book ws
Pgs. 88-90,
#'s 2, 4, 5, 7, 10, 17, 19, 26, 29, 33, 35, 39, 43, 48, 56 and limits at infinity ws