AP Calculus AB - Worksheet 27
Derivatives of ln and e
Know the following theorems:
1.
2.
Examples
1.
Find
2.
3.
.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17. A line with slope m passes through the origin and is tangent to
18. Evaluate
. Wha
AP Calculus AB Infinite Limits and Finding Asymptotes
What is an Infinite
Limit?
When a function, f, INCREASES without bound or DECREASES without
bound as x approaches a target value, c, then the limit is called an
INFINITE LIMIT. The notation is:
OR
This
AP Calculus
The Derivative and the Tangent Line Problem
Origins of Calculus (17th
century Europe)
Solve 4 major problems:
1.
2.
3.
4.
The
The
The
The
tangent line problem.
velocity and acceleration problem.
minimum and maximum problem.
area problem.
Solvi
AP Calculus AB Product Rule for Differentiation
Investigation
Let f(x) = x3 and g(x) = x5
Then f(x) =
and g(x) =
(Power Rule)
If h(x) = f(x) * g(x), is h(x) = f(x) * g(x) ?
h(x) =
h(x) =
So how do you find
the derivative of a
product?
=
Product Rule
The d
AP Calculus AB Quotient rules
Quotient Rule
Proof using the
definition of a
derivative.
Example:
Rewrite 1st!
Y=
Derivatives of Trig
Functions
(use Quotient Rule
to derive formula.)
Simplifying
Answers after
differentiating
Two Rules: NO negative exponent
Calculus Cheat Sheet
Limits
Definitions
Precise Definition : We say lim f ( x ) = L if
Limit at Infinity : We say lim f ( x ) = L if we
x a
x
for every e > 0 there is a d > 0 such that
whenever 0 < x - a < d then f ( x ) - L < e .
can make f ( x ) as clo