# Calculus I

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 Author: clkottke ID: 149285 Filename: Calculus I Updated: 2012-04-22 15:47:04 Tags: calculus Folders: Description: Calculus I part 1, limits Show Answers:

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1. Formula for Average Velocity
2. The slopes of the _______ line is the ______ of the slopes of the secant lines.
• tangent
• limit
3. The slope of the tangent equals _______________
instantaneous velocity

4. if and only if _________ and __________

5. The line x=a is called a vertical symptote of the curve y = f(x) if at least one of the following is true: (6)

6. Limit Laws

Suppose that c is a constant and the limits

and

exist, Then:

if
• c
• The limit of a constant is the constant
7. =
where n is a positive integer
if n is even, we assume that a > 0.

8. where n is a positive integer
if n is even, we assume that
9. If a polynomial or a rational function and a is in the domain of f, then

10. If for all x in an open interval that conatins a (except possibly at a) and the limits of f and g both exist as x approaches a, then
11. Squeeze theorem:

If for all x in an open interval that contains a (except possibly at a) and

THEN:
12. Let f be a function on some open interval that contains the number a, except possibly at a itself.

if for every number > 0 there is a corresponding number > 0 such that:
|f(x) - L| < whenever 0 < | x - a| <
13. Definition of Left-Hand Limit

if for every number > 0 there is a corresponding number > 0 such that:
|f(x)-L| < whenever < x < a
14. Definition of Right-Hand limit

if for every number > 0 there is a corresponding number > 0 such that:
|f(x) - L| < whenever a < x < a +
15. When a limit = 1/0 it is:
undefined
16. When a limit = 0/0 it is
Indeterminate

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