Exam
N ame_
M U L T IPLE C H O I C E. C hoose the one al ternati ve that best co mp letes the statement or answ ers the q uestion.
T he grap h o f a f unct ion is g i ven. C hoose the answ er that rep
201-103-RE - Calculus 1
WORKSHEET: LIMITS
1. Use the graph of the function f (x) to answer each question.
Use 1, 1 or DN E where appropriate.
(a)
f (0) =
(b)
f (2) =
(c)
f (3) =
(d)
(e)
(f)
(g)
(h)
li
5.3 Solving Trig Equations - Worksheet #2 Name:
Pre-calculus Date: Block: _
art 1: Solve for the unknown variable. Give all of the exact general solutions.
J5
1. sin6=7 2. cos6=sin0 3. tan6=1
I
4. l+s
Worksheet - Difference Quotient
Name:_
If
then
line 1
f(x) = 3x2 2x
f (!) = 3!2 - 2!
Whatever is in this position becomes the exact replacement for x each place it
appears in the right side of the f
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
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 limi
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 pr
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
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
Answer
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