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Chest and Back
By Zoe Rodriguez
Copyright 2015
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Table of Contents
Not For Resale .4
Disclaimer .5
About the
12.3-Sonya Bilbrey
1 of 2
https:/xlitemprod.pearsoncmg.com/api/v1/print/math
Student: Sonya Bilbrey
Date: 2/23/17
Instructor: Ashley Dyer
Course: Math 1325-004, Spring 2017
Assignment: 12.3
1. Write the function as a composition of two functions.
4
7
2
y=
Caleb Baumert 3rd
Step-by-step solution:
Explanations of steps taken:
Subtract 13 from both sides,
Begin completing the square,
Take half from middle term and square it,
Square root both sides to make squared sign
disappear,
Add 4 to both sides
Use +/- on
College Algebra
FOCUS! Section 3.3
Student: _
Date Due: _
1.) Find all zeros of the polynomial function. Then
state their multiplicities.
3.) One zero is given for the polynomial function.
Find all other zeros.
0 B #BB #$ B %#
0 B %B$ 'B# #B ";
Zero
Multi
College Algebra
FOCUS! Section 3.4
Student: _
Date Due: _
1.) Use transformations to graph the function
carefully.
3.) Graph the polynomial function by plotting zeros
and sketching appropriate end behavior.
0 B B "$ %
0 B #B$ &B# B '
Zero
2.) Describe the
College Algebra
FOCUS! Section 3.5
1.) Write the equations of the vertical and
horizontal asymptotes for the given rational function.
State the domain in interval notation.
0 B
%B# %B #%
B# $B "!
Student: _
Date Due: _
3.) Write the equations of the vert
College Algebra
FOCUS! Section 3.1
Student: _
Date Due: _
1.) Use the function 0 B B # $
to find the following:
a.) the vertex
3.) Brigette Cole has a taco stand. She has found
that her daily costs are approximated by the function
GB B# %!B '"!, where GB
College Algebra
FOCUS! Section 3.2
1.) Use synthetic division to perform the division.
&B% &B$ #B# B $
B"
Answer: _
Student: _
Date Due: _
3.) Use synthetic division to decide whether the
given number 5 is a zero of the polynomial
function.
0 B %B% B# "(B
Pre-algebra: You will need to a wide
variety of pre-algebraic functions. You
should definitely know how to do
operations containing whole numbers,
decimals, fractions, integers, place value,
square roots and approximations, the
rules and concept of expone
12.8 Lab - Length of Curves
Student: _
Calculus III
1.) Find the lenth of the entire spiral < /+) , where ) 0 and + !.
1.) _
2.) A cycloid is the path traced by a point on a rolling circle (think of a light on the rim of a moving bicycle
wheel). The cyclo
Lab 13.8 - Maximum/Minimum Problems
Student: _
Calculus III
Based on the level curves that are visible on the following graphs, identify the approximate locations of the
local maxima, local minima, and saddle points. Express the locations as ordered pairs
Conic
Parabola
Equation
B 2 # %:C 5
C 5# %:B 2
Ellipse
B 2 #
C 5 #
"
+#
,#
B 2 #
C 5 #
"
,#
+#
Hyperbola
B 2 #
C 5 #
"
+#
,#
C 2 #
B 5 #
"
+#
,#
Properties
Orientation: Vertical (Up if : !, Down if : !)
Vertex: 2 5
Distance from center to focus
Lab 14.3 - Double Integrals in Polar Coords.
Student: _
Calculus III
1.) Carefully sketch the region in Quadrant I outside the circle < # and inside the lemniscate
< #-9=#). Then find the exact value of the area using a double integral in polar coordinate
Lab 14.1 - Double Integrals Over Rectangles
$C
.B .C
B C#
! "
"
1.)
Evaluate exactly:
Student: _
Calculus III
%
1.) _
2.) Choose the best order to evaluate B=/- # BC .E
forV B Cl! B 1$ ! C ".
2.) _
V
Draw the solid whose volume is given by
#
3.)
!
!
"
12.3 Lab - Dot Products
Student: _
Calculus III
1.) Find the angle between the vectors v $ & # and
u * & " to the nearest degree.
1.) _
2.) Determine the work done if a suitcase is pulled 50 ft along a flat sidewalk
with a constant force of 30 lbs at an a
12.6 Lab - Calculus of VVFs
Student: _
Calculus III
Let the position of an object moving in three dimensional space be given by r> B> C> D > , for
> !. The velocity of the object is v> rw > Bw > Cw > D w > . The speed of the object is the Realvalued funct
Lab 13.1A - Conics Review
1.) Construct the graph of B
C#
4.
Student: _
Calculus III
Clearly plot the vertex, the directrix, and the focus.
Vertex: _
Directrix: _
Focus: _
2.) Construct the graph of "'B "# *C "# "%. Carefully plot the center, major and m
Lab 14.2 - Double Integrals over General Regions
Student: _
Calculus III
1.) Find the exact area of the region bounded by the curves C ( (=38B and C ( (=38B over the
interval ! 1 using a double integral. Carefully sketch the area in the space below.
1.) _
12.9 Lab - Curvature and Normal Vectors
Student: _
Calculus III
1.) Determine the curvature of the trajectory given by r> >, %># at > !. What is the
corresponding radius of curvature?
,! _
Radius: _
2.) The driver of a car follows the parabolic trajectory
12.5 Lab - Lines and Curves in Space
Student: _
Calculus III
1.) Determine the parametric equations of the line through the points
T # " # and U % & !.
2.) Determine the points (if they exist) at which the plane B C !
intersects the curve <> cos > sin > >
Lab 13.2 - Graphs and Level Curves
Student: _
Calculus III
1.) Match the graphs and functions below. Write the correct letter of the graph in the blank next to the
function.
_ 0 B C -9=BC
_ 1B C 68B# C#
_ 2 B C
"
BC
_ :B C
"
" B# C#
2.) Match the graph
12.2 Lab - Vectors in Three Dimensions
Student: _
Calculus III
1.) A fisherman wants to know if his fly rod will fit in a rectangular 2 ft x 3ft x 4 ft packing box. What is the
longest rod that fits in this box?
1.) _
2.) A small plane is flying horizonta
Lab 14.5 - Triples in Cylindrical, Spherical Coords
Student: _
Calculus III
1.) Use a triple integral in rectangular coordinates to find the volume of the region bounded by the parabolic
cylinder C B# and the planes D $ C and D !.
1.) _
2.) Use a triple i
Lab 13.9 - LaGrange Multipliers
Student: _
Calculus III
1.) The following figure shows the level curves of 0 and the constraint curve 1B C !. Estimate the
maximum and minimum values of 0 subject to the constraint. At each point where an extreme value occu
Lab 13.6 - Directional Derivatives, Gradient
Student: _
Calculus III
1.) You and a friend are standing on the surface of hilly terrain described by 0 B C -9=B C. Suppose
you are located at point T ! 1 " and your friend is located at point U 1# ! !. What i
Lab 13.1B - Quadric Surfaces
Student: _
Calculus III
The standard form of a quadric surface is given in each problem. Identify the surface as an ellipsoid, elliptic
paraboloid, hyperbolic paraboloid, elliptic cone, hyperboloid of one sheet, or hyperboloid
Lab 13.4 - Partial Derivatives
Student: _
Calculus III
1.) Consider the ideal gas law T Z 5X , where 5 ! is a constant.
a.) Determine the rate of change of volume with respect to pressure
at constant temperature. Does volume increase, decrease, or
remain
12.4 Lab - Cross Product
Student: _
Calculus III
For full credit on graphs, clearly label the coordinate axes and scales.
1.) Let u ! # # and v ! # # . Determine
u v. Then, sketch and label u, v, and u v on the graph.
2.)
a.) Graph the parallelogram with
Lab 14.4 - Triple Integrals
Student: _
Calculus III
1.) Find the volume of the wedge of the cylinder B# #&C# #& created by the planes D % B and
D B % using a triple integral in rectangular coordinates.
1.) _
2.) Find the volume of the cap of a sphere with
Lab 14.7 - Change of Variables in Multiple Integrals
Student: _
Calculus III
Evaluate /BC .E, where V is the region bounded by the hyperbolas BC " and BC % and the lines
V
CB " and CB $ by completing the problems below.
1.) Very carefully sketch the regio