Mia Montilla
MA 118
Quiz 1
Return a Word document with answers, e-mail to Professor Nelan ([email protected]). Due:
May 28, at 12:00 Midnight EST. Open book, open note.
1) Write as x to some power ( xp)
2) Simplify:
(5 x3 y)2
21,600
3) Simpli
Example 1 Determine if each of the following are functions.
(a)
(b)
Solution
(a) This first one is a function. Given an x, there is only one way to square it and then add 1 to the result. So,
no matter what value of x you put into the equation, there is o
Mia Montilla
Maria Sokolovic
Ron Mule
Tullio Ossa
Anthony Moschella
MA 118
Bonus Quiz
Return as a Word document with answers. Due: July 2, at 10:00 p.m. (no
exceptions).
1) Assume the value of a car is a linear function of time. When new, the car
is worth
MA 118
Quiz 4
Do not bother to algebraically simplify the derivatives you compute. I need
one quiz from each group. Designate one member to hand the quiz in.
Make sure the names of all group members appear on the answer sheet. Due
by June 16, midnight
1)
Study guide for test 2 (2.1 through 2.4):
Use sum/difference rule to find a derivative
Use product rule to find the derivative
Use quotient rule to find the derivative
Find the rate of change in a word problem
Take the limit of an expression
No limits inv
Mia Montilla
MA 118
Quiz 5
Due by midnight, June 24. I want one answer sheet from each group.
1) Find the domain and range of the function f(x) = ex 2
i. Domain: (-,)
ii. Range:(2,)
2) Find the domain and range of the function: f(x) = ln ( x - 2)
i. Domai
Exponential / Logarithm Equation Notes:
Well start with equations that involve exponential functions. The main property that well need for these
equations is,
Example 1 Solve
.
Solution
The first step is to get the exponential all by itself on one side of
Tangent Line Notes:
Tangent Lines
The first problem that were going to take a look at is the tangent line problem. Before getting into this
problem it would probably be best to define a tangent line.
A tangent line to the function f(x) at the point
is a l
Critical Points Notes:
Critical points will show up throughout a majority of this chapter so we first need to define them and work
a few examples before getting into the sections that actually use them.
Definition
We say that
following are true.
is a crit
MA 118 Exam 4 Review
1. If a college education costs $125,000, how large a trust fund must be established at a childs
birth paying 4.5% compounded continuously to ensure sufficient funds at age 18? (round to
the nearest dollar)
2. Find each logarithm.
a.
MA 118 Test 2 Review
1. Evaluate the following limits
2
a. lim( x 5 x 7)
x 3
x 2 2 x 15
lim
b. x 5
x 5
1
x
c. lim1 x
x 0
2. Find the equation of the line tangent to the curve f ( x) x 3 at x = 2.
3. Calculate the derivatives of the following functions
Final Exam Review
1. Evaluate the following limits. Round answers to two decimal places.
3
a. lim ( x 5 x 4)
x 2
x 2 x 12
b. lim
x 4
x 4
1
x
c. lim1 x
x 0
2. Find the equation of the line tangent to the graph of the function f ( x ) 3e ( x
2
4)
at
MA 118 Exam #3Review
For each function in questions 1-3:
a. Make a sign diagram for the first derivative.
b. Make a sign diagram for the second derivative.
c. Sketch the graph by hand, showing all relative extreme points.
1.
f ( x) x 3 3 x 2 9 x 7
2.
f (
MA 118 Review Sheet
In exercises 1 4 reduce solve for x.
1. 5 x 23 2 x 1
2.
3
2
x 4 x
3. 3 x 4 5 x 7
4.
(2 x 8)(5 x)
0
x 2 6 x 9
5. Find the slope of the line determined by the points
a. (-1, 4) and (5, 1)
b. (6, -4) and (6, -3)
6. Draw the line 3x - 2y =
Name:
Date:
MA 118 Derivatives Worksheet
Find the derivative of each function.
1.
f ( x) x 5
2.
f ( x)
3.
Use the product or the quotient rule to find
each derivative
11. y 3x 1 2 x 2 5 x
1
x4
1
1
12. g ( x) 1 2
x
x
f ( x) x
4. g ( x) x 3 2 x
13. f (