1. Section 1.5 - Infinite Limits

2. Infinite Limits:
As the denominator approaches zero, the value of the fraction gets very large.
vertical asymptote at x=0.
If the denominator is positive then the fraction is positive.
If the denominator is negative then the fraction is negative.

3. Infinite limits Definition: The notation
(read as “the limit of f(x) , as x approaches a, is infinity”)
means that the values of f(x) can be made arbitrarily large by taking x sufficiently close to a (on either side of a) but not equal to a.
Note: Similar definitions can be given for negative infinity and the one-sided infinite limits.
Example:

4. Example:
The denominator is positive in both cases, so the limit is the same.
So as the denominator gets infinitesimally small (towards 0), the fraction gets infinitesimally large (∞) .
The key to thinking about this is
that as the denominator in a fraction
gets larger, the fraction gets smaller
and as the denominator gets smaller,
the fraction gets larger.

5. Vertical Asymptotes
Definition: The line x=a is called a vertical asymptote of the curve y=f(x) if at least one of the following statements is true:
Example:
x=0 is a vertical asymptote for y=1/x2

6. Determine all vertical asymptotes and point
discontinuities of the graph of
Note: we have a
vertical asymptote
at x = 1 and a point
discontinuity at
x = -3
lim as x ?
lim as x from L&R?

7. Properties of Infinite Limits
1. Sum or difference
2. Product
3. Quotient

8. HW Pg , odds, 61