MAT 125 Exam 2 Review
Released November 3, 2010
1. Find the derivatives of the following functions. (a) sin(x2 ex ) (b) arctan( 5x + 4) (c) ln x+2 3x + 4 (d) esin(x)+cos(x) ex + ex (e) x e ex x2 + 4 x + 3 (f) x3 + 1 (g) arcsin 1+x 1x
(h) log6 (x2 + 5x) (i
MAT125 Fall 2013 Review for Midterm I
1.1 Understand the definition of function (box, p. 12) and the importance
of the word exactly. The Vertical Line Test (p. 17) shows exactly what
exactly means in terms of graphs (Exercises 5-8). Be able to ascertain t
MAT 125 Fall 2016
Name_
Kahn
Bernhard
Recitation_
Wertz
_
Paper Homework #5
1)
Find the derivatives of the following functions (2 points each):
(a)
f x x 2e1 x
(b)
x t sin 2 t cos 2 t
(c)
g x
2
4 x
4 x
(d)
f 5 sec
(e)
f x sin cos 2 x 5
MAT125, Paper Homework Cup
1. Let f (x) = x +
x.
(a) Write a limit which represents the derivative of f (x).
(b) Evaluate the limit.
2. Coffee is being poured into the mug shown at right at a constant rate (that
is, a constant volume of coffee per unit of
MAT126, Paper Homework GA
1. Let f (x) be given by the function whose graph is shown below.
Z
2
(a) Calculate
f (x) dx. Justify your answer.
2
Z
8
f (x) dx. Justify your answer.
(b) Calculate
0
2. Write a definite integral which corresponds to the limit
MAT125, Paper Homework Lim
1. Calculate
lim
x0
1
1
2
x x +x
,
if it exists. (If the limit doesnt exist, explain.)
2. Let F (x) =
x2 4
.
|x 2|
(a) Compute lim+ F (x) and lim F (x).
x2
x2
(b) Does lim F (x) exist? Justify your answer, and sketch the graph
/-\ Intro Calc More Optimization Practice
1. A rectangular storage area with an open top is to have a volume of g. The length of
its base is twice the width. What are the dimensions of the box with minimum
surface area?
- SA = gleam + why we
1L
Qw h \N ':
Secant vs Tangent on a Curve
P
P
Q
secant line
tangent line
Equation of Tangent Line
Section 2.1
Want to find the equation of the tangent line that passes through a given point on a function curve.
P1
In general, to find the equation of a line, need to kn
Review Evaluating Limits
2
2
3(1)
4(1) 9 2
3
x
4
x
9
lim
x1
x3 3
23 3 8 3
=
=
5
lim
x 2
x 1
2 1
1
ok
( x 5)( x 1)
x2 6x 5
lim x 1 5 1 4
lim
lim
x5
x5
x5
x 5
x 5
5-5 = 0
2
9
6
h
h
9
h(6 h)
(3 h) 9
lim 6 h 6 0 6
lim
lim
lim
h 0
h 0
h 0
h
h
h 0
h
2
Ev
MAT125
Section 3.1
Intro
Section 3.1
So far, we have learned that a function has a derivative that
tells about the rate of change between the independent variable x and
the dependent variable y.
The derivative can be measured using the slope of the tangen
MAT125
Sections 2.6, 2.7, 2.8
Rate of Change
mPQ
The slope of a tangent line at a point on a curve measures
the rate of change at that point
f ( x) f (a)
xa
use a limit to minimize distance between x and a:
f ( x) f (a )
m lim
x a
xa
DEFINITION #1
Second
is defined as
Relations/Functions
Function:= a rule that assigns each x-value to exactly one y-value
Relations
(this relation looks at ordered pairs)
denote a set with curly braces
(x,y)
cfw_( A,1) , ( B,12), (C ,5)
is a function
example of relation that
MAT 125
Solutions to Midterm 2 (Fezzik)
1. For each of the functions f (x) given below, find f 0 (x).
4 points
1 + 2x2
1 + x4
Solution: This is a straightforward quotient rule problem:
(a) f (x) =
f 0 (x) =
(4x)(1 + x4 ) (1 + 2x2 )(4x3 )
4x 4x3 4x5
=
(1 +
MAT 125
Second Midterm
April 7, 2016
Name:
ID:
Rec:
Question:
1
2
3
4
5
6
7
Total
Points:
12
12
12
14
12
12
12
86
Score:
There are 7 problems in this exam. Make sure that you have them all.
Do all of your work in this exam booklet, and cross out any work
Homework
All homework is due by 10 AM on its due date. You can either hand in the
homework in recitation, or put it in the TAs mailbox.
Assignment 1:
See Blackboard for the Homework problems
This assignment is due on September 5, 2014.
Assignment 2:
Chap.
MATH 125
Name:
Second Midterm
March 20, 2007
ID:
Rec:
Question: Points: Score:
1 12
2 12
3 8
4 8
5 16
6 14
7 10
8 10
Total 90
There are 8 problems in this exam, printed on 6 pages (not including this cover sheet). Make sure that you have them all. Do all
Practice Final Exam
MAT 125
Fall 2014
The actual exam will consist of eight problems
1. Compute the following limits. Please distinguish between lim f (x) = , lim f (x) =
and limit does not exist even allowing for infinite values.
(a) lim x2 + x 1
x1
x2
MAT125A Fall 2014
Practice Midterm II
The actual exam will consist of six problems.
Problem 1
Compute the following limits. Please distinguish between limit is equal to , limit is equal
to and the limit doesnt exist even allowing for infinite values:
1. l
MAT125A Fall 2014
Practice Midterm I
The actual exam will consist of six problems.
Problem 1
Suppose f (x) is a linear function such that f (1) = 1, f (3) = 6. Then f (1) =?
a) 3/4, b) 3/2, c) 5/2, d) 3/4, e) 2, f ) none of these.
Problem 2
Express the fo
1 . If f(0) = 3, use the graph of the following equation to sketch f. In your sketch, pay attention to
concavity. Accurate y values are not required.
2/ = M) = — 1
, I -X
aw vs" W“ ‘1":“4 ’5 ‘9
[4,; 914‘! jui‘e “X _.—- u. ‘mww www—
«LLINCQE-M ' r m. w
-_
MAT 125 (REVIEW)-EXAM #2-Fall 2015
NAME:
TA Name:
When do you have recitation?
Each numbered question is worth 20 points.
1 . If f(0) = 3, use the graph of the following equation to sketch f. In your sketch, pay attention to
concavity. Accurate y values a
*Each numbered question is worth 20 points.
1. For all parts in question #1 = ﬁ€_31
a.) Find the slope of the tangent line on f at x=1.
in); (W): ix»: w -m—
: Q”3>(< gli’ 3V6C>
,3 _
dope af’Xzi: 4H0): 6 (EL-g) . -
b) Write an expression for f’ (x).using
MAT 125-Final Exam Part 1(SAMPLE)-Fall 2015
NAME:
TA Name:
When do you have recitation?
This exam is pass/fail. You must score 9 out of 12 to pass.
1. Find the absolute minimum of f (x) = x2
2. Find the derivative of
p
3 + ex
4x for 1
ln(8 + 6x)
1
x
3.
3.
MAT 131- midterm
(sample test)-Summer
2013
NAME:_
Each numbered question is worth 20 points.
1. For all parts in question #1 f (x) =
p
xe
3x
a.) Find the slope of the tangent line on f at x=1.
b) Write an expression for f 0 (x):using the dention of the de