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MA 171
Fall 2016 - Lenahan
Test 3 - 100 pts.
Name:
Answer the questions below showing all work on the test paper. You will be graded on the correctness of
your answer as well as the correctness of your method.
1. Evaluate the integrals.
Z
(a)
sec2 5 d
Z
(
MA 171
Fall 2016 - Lenahan
Test 2 - 100 pts.
Name:
Answer the questions below showing all work on the test paper. You will be graded on the correctness of
your answer as well as the correctness of your method.
What is the exact value of tan1 (1)?
1.
(a)
(
MA 171
Fall 2016 - Lenahan
Test 4 - 100 pts.
Name:
Work Out: Show all work. You will be graded on the correctness of your method as well as the
correctness of your answer.
(34) 1. Graph f (x) using the appropriate curve sketching techniques. Give interval
Lab 14 - Arclength
Goals
To develop the idea of approximating arc length by the sum of the lengths of straight line
approximations to the curve
To compute arc length using an integral.
Before the lab
The idea of the arc length of a curve is very easy to
MA 171
Fall 2016 - Lenahan
Test 1 - 100 pts.
Name:
Answer the questions below showing all work on the test paper. You will be graded on the correctness of
your answer as well as the correctness of your method.
(8) 1. Find the domain of the function f (x)
CALCULUS A REVIEW SHEET
Derivative Definition
Basic Properties of Derivatives
LHopitals Rule
Limit Properties
Product Rule
Quotient Rule
Common Derivative Formulas
Power Rule
Chain Rule
CALCULUS B REVIEW SHEET
Integral Definition
Fundamental Theorem
Integ
Use the divergence theorem to evaluate
where
and the
surface consists of the three surfaces,
,
on the top,
on the sides and
,
on the bottom.
The region E for the triple integral is then the region enclosed by these surfaces.
Note that cylindrical coordina
TEST 2
REVIEW
MA 171-04
Spring 2017
*Notice that the trig derivatives that begin
with c are all negative! Isnt that handy?!
ABSORB THIS
INFO!
Product/Quotient Rule
EXAMPLES
EXAMPLES
The Quotient Rule Song
Low, D High Minus High, D low all over Low Low
But
Test 4 Review
MA 171-04 Spring 2017
Sketching a Graph with Calculus
Indeterminate forms
Steps to Sketching a Graph with
Calculus
1. Take the Derivative of the function given
2. Find what x values make the derivative go to 0 or
undefined. (set it equal to
LAB REPORT
*If you have a laptop, you may substitute sketch the graph on your paper below with take a screen
shot and insert the picture into a document with the rest of your answers. This document can be emailed to me as your lab report. Be sure all name
Alex Stroud
Helen Sakatis
Calculus A
31 August 2016
1a.
1b.
1c. At x=2, the y-value will
X=1.8=11.872
x=2.1=16.771
approach 15.
X=1.9=13.369
x=2.01=15.171
X=1.99=14.831
x=2.001=15.017
X=1.999=14.983
x=2.0001=15.002
X=1.9999=14.998
x=2.00001=15.0001
1a. Th
In order to work with surface integrals of vector fields we will need to be able to write down
a formula for the unit normal vector corresponding to the orientation that weve chosen to
work with. We have two ways of doing this depending on how the surface
Stokes Theorem
Let S be an oriented smooth surface that is bounded by a simple, closed, smooth boundary
curve C with positive orientation. Also let
evaluate
be a vector field then,
wher
e
the part of
Assume that S is oriented upwards.
and S is
above the p
MTH 126 Calculus II
Sample Final Exam
1. Find the volume of the solid formed by revolving the region bounded by the graphs of
y x 2 2, y 2, x 0, and x 3 about the x axis . Use the Disk Method.
y x 2 and y 4 x x 2
2. Use the Shell Method to find the volume
1.
A. sin(1/x)
On this graph, the sin function continues oscillating between -1 and 1 and therefore the limit as
x approaches 0 does not exist. While this graph does not show it, f(x) does not exist at 0
because an x value of zero would result in an undef
Lab 6: Indeterminate Limits and lHopitals Rule
1.
For a, b, and e, the limit theorem does apply, and the answers are written above. For c, the limit does
not apply because the bottom is zero. This means that the limit is infinity. For d and f, the form is
Lab 1: Graphing Functions
1.
2.
a.
a. When changing the value of b in y=3x 2+bx2, the vertex of the graph moves down and
to the left.
b. When the value of b in
y=3x2+bx-2 is negative, the
graph moves down and to
the right.
c. The value of b moves the
vert
Lab 7: Riemann Sums and the Definite Integral
2. a.
b.
When using the
N=
Left
Right
20
34.8
37.2
10
33.6
38.4
60
35.6
36.4
100
35.76
36.24
Riemann sum
function of maple, the
left sum is 35.4, which is .6 values away from
36, the real area. The
right sum i
Original graph and tangent line at x=2
dx=0.1
dx=0.5
dx=0.01
Lab #5: Problem 44
Original function:
f(x)=x3-2x+3
Derivative of function: f(x)=3x2-2
Tangent line at x=2:
dx
0.1
0.5
0.01
x
2.1
2.5
2.01
y=10x-13
8
12
7.1
y=10x-13
f(x)=x3-2x+3
8.061
13.625
7.1
Lab 9: Newtons Method
2. a)
f(x) =
3
2
x 4 x 1
X Value
Root
X0 = 5
151
35
X1 =
151
35
4.087
X 2 = 4.087
4.061
X 3 = 4.061
4.061
b)
c)
The black, red, and blue graphs are so close that you cant see the different graphs, which means that
this is a very clos
Lab #3 9/15/15
2. a) f(x) = x2(x2-1)(x+2)
f(x) = 5x4+8x3-3x2-4x
b) [-2.5,-1.6] U [-0.6,0] U [0.8,1.5]
c) [-2.5,-1.6] U [-0.6,0] U [0.8,1.5]
d) [-1.6,-0.6] U [0,0.8]
e) [-1.6,-0.6] U [0,0.8]
f) x = -1.6, -0.6, 0, 0.8
g) x = -1.6, -0.6, 0, 0.8
3. a)
f(x) =
Trigonometry Formulas _ tanA + tanB
(A +B)1tanAtanB
. . . . . y _ _ tanA tanB
1. Denitions and Fundamental Identities tan (A B) 1 + tan A tan B
Sine: sin6 = = P(x, y)
r 0306 %h sin(A 7;) = cosA, cos(A 727) = sinA
Cosine: cos 6 = g = #6 A x 11' 11'
set: si
CALCULUS A REVIEW SHEET
Derivative Definition
Basic Properties of Derivatives
LHopitals Rule
Limit Properties
Product Rule
Quotient Rule
Common Derivative Formulas
Power Rule
Chain Rule
CALCULUS B REVIEW SHEET
Integral Definition
Fundamental Theorem
Integ
The limit of a secant line as
x x approaches zero is a
2
1
True or False:
A Limit is an approximation
of the x-axis value as it
relates to the y axis value
The formula for Average
Rate of Change:
List the 2 cases when there
exists a vertical asymptote:
Hi
University of Alabama in Huntsville Math 2447 Fall 2012
Midterm #1
Full Name: . Signature .
, Note: You need to give Justication to all your Answers in order to have full CREDIT.
Exercise 1. (30 points) Answer each of the following by TRUE or FALSE. Jus-
University of Alabama in Huntsville
Math 244, SPRING 2012
Midterm #2
Full Name: . Signature.
Note: You need to give Justification to all your Answers in order to have full CREDIT.
Exercise 1. (40 points) Answer each of the following by TRUE or FALSE. Just