THOMAS' CALCULUS (LL)>>CUSTOM< PKG<
14th Edition
ISBN: 9781323837689
Author: WEIR
Publisher: PEARSON C
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Chapter 1.1, Problem 68E
(a)
To determine
Calculate the y-coordinate of P in terms of x.
(b)
To determine
Calculate the area of the rectangle in terms of x.
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2. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.015.
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)
ASK YOUR TEACHER
3
1
3 +
dy, n = 6
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule
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This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3πt)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot (3πt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1
(d) Express the slope of the rod…
4. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.024.
Find the approximations Tη, Mn, and S, to the integral
computer algebra system.)
ASK YOUR TEACHER
PRACTICE ANOTHER
4 39
√
dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a
n
Tn
Mn
Sp
6
12
n
ET
EM
Es
6
12
What observations can you make? In particular, what happens to the errors when n is doubled?
As n is doubled, ET and EM are decreased by a factor of about
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'
and Es is decreased by a factor of about
Chapter 1 Solutions
THOMAS' CALCULUS (LL)>>CUSTOM< PKG<
Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - In Exercise 1–6, find the domain and range of each...Ch. 1.1 - Which of the graphs are graphs of functions of x,...Ch. 1.1 - Which of the graphs are graphs of functions of x,...Ch. 1.1 - Prob. 9ECh. 1.1 - Express the side length of a square as a function...
Ch. 1.1 - Express the edge length of a cube as a function of...Ch. 1.1 - A point P in the first quadrant lies on the graph...Ch. 1.1 - Consider the point (x, y) lying on the graph of...Ch. 1.1 - Consider the point (x, y) lying on the graph of ....Ch. 1.1 - Find the natural domain and graph the functions in...Ch. 1.1 - Find the natural domain and graph the functions in...Ch. 1.1 - Find the natural domain and graph the functions in...Ch. 1.1 - Find the natural domain and graph the functions in...Ch. 1.1 - Functions and Graphs
Find the natural domain and...Ch. 1.1 - Functions and Graphs
Find the natural domain and...Ch. 1.1 - Find the domain of .
Ch. 1.1 - Find the range of .
Ch. 1.1 - Graph the following equations and explain why they...Ch. 1.1 - Graph the following equations and explain why they...Ch. 1.1 - Graph the functions in Exercise.
Ch. 1.1 - Piecewise-Defined Functions
Graph the functions in...Ch. 1.1 - Graph the functions in Exercise.
Ch. 1.1 - Piecewise-Defined Functions
Graph the functions in...Ch. 1.1 - Find a formula for each function graphed in...Ch. 1.1 - Find a formula for each function graphed in...Ch. 1.1 - Find a formula for each function graphed in...Ch. 1.1 - Find a formula for each function graphed in...Ch. 1.1 - For what values of x is
Ch. 1.1 - What real numbers x satisfy the equation
Ch. 1.1 - Does for all real x? Give reasons for your...Ch. 1.1 - Graph the function
Why is f(x) called the integer...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - Graph the functions in Exercise. What symmetries,...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - In Exercise 47–62, say whether the function is...Ch. 1.1 - The variable s is proportional to t, and s = 25...Ch. 1.1 - Kinetic energy The kinetic energy K of a mass is...Ch. 1.1 - The variables r and s are inversely proportional,...Ch. 1.1 - Boyle’s Law Boyle’s Law says that the volume V of...Ch. 1.1 - A box with an open top is to be constructed from a...Ch. 1.1 - The accompanying figure shows a rectangle...Ch. 1.1 - In Exercises 69 and 70, match each equation with...Ch. 1.1 - y = 5x
y = 5x
y = x5
Ch. 1.1 - Graph the functions f(x) = x/2 and g(x) = 1 +...Ch. 1.1 - Graph the functions f(x) = 3/(x − 1) and g(x) =...Ch. 1.1 - For a curve to be symmetric about the x-axis, the...Ch. 1.1 - Three hundred books sell for $40 each, resulting...Ch. 1.1 - A pen in the shape of an isosceles right triangle...Ch. 1.1 - Industrial costs A power plant sits next to a...Ch. 1.2 - In Exercises 1 and 2, find the domains of f, g, f...Ch. 1.2 - In Exercises 1 and 2, find the domains of f, g, f...Ch. 1.2 - In Exercises 3 and 4, find the domains of f, g,...Ch. 1.2 - In Exercises 3 and 4, find the domains of f, g,...Ch. 1.2 - If f(x) = x + 5 and g(x) = x2 − 3, find the...Ch. 1.2 - If f(x) = x − 1 and g(x) = 1/(x + 1), find the...Ch. 1.2 - Prob. 7ECh. 1.2 - In Exercises 7–10, write a formula for .
8.
Ch. 1.2 - In Exercises 7–10, write a formula for .
9.
Ch. 1.2 - In Exercises 7–10, write a formula for .
10.
Ch. 1.2 - Let f(x) = x – 3, , h(x) = x3and j(x) = 2x....Ch. 1.2 - Prob. 12ECh. 1.2 - Copy and complete the following table.
Ch. 1.2 - Copy and complete the following table.
Ch. 1.2 - Evaluate each expression using the given table...Ch. 1.2 - Prob. 16ECh. 1.2 - In Exercises 17 and 18, (a) write formulas for f ∘...Ch. 1.2 - Prob. 18ECh. 1.2 - 19. Let . Find a function y = g(x) so that
Ch. 1.2 - Prob. 20ECh. 1.2 - A balloon’s volume V is given by V = s2 + 2s + 3...Ch. 1.2 - Use the graphs of f and g to sketch the graph of y...Ch. 1.2 - The accompanying figure shows the graph of y = –x2...Ch. 1.2 - The accompanying figure shows the graph of y = x2...Ch. 1.2 - Match the equations listed in parts (a)–(d) to the...Ch. 1.2 - The accompanying figure shows the graph of y = –x2...Ch. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - Exercises 27–36 tell how many units and in what...Ch. 1.2 - Prob. 35ECh. 1.2 - Tell how many units and in what directions the...Ch. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Prob. 39ECh. 1.2 - Prob. 40ECh. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Graph the functions in Exercises 37–56.
52.
Ch. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Prob. 55ECh. 1.2 - Prob. 56ECh. 1.2 - The accompanying figure shows the graph of a...Ch. 1.2 - The accompanying figure shows the graph of a...Ch. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Vertical and Horizontal Scaling
Exercises 59–68...Ch. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Tell in what direction and by what factor the...Ch. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Graphing
In Exercises 69–76, graph each function...Ch. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - Graphing
In Exercises 69–76, graph each function...Ch. 1.2 - Prob. 73ECh. 1.2 - Prob. 74ECh. 1.2 - Prob. 75ECh. 1.2 - Graphing
In Exercises 69–76, graph each function...Ch. 1.2 - Prob. 77ECh. 1.2 - Prob. 78ECh. 1.2 - Prob. 79ECh. 1.2 - Prob. 80ECh. 1.2 - Prob. 81ECh. 1.2 - Prob. 82ECh. 1.3 - On a circle of radius 10 m, how long is an arc...Ch. 1.3 - A central angle in a circle of radius 8 is...Ch. 1.3 - You want to make an 80° angle by marking an arc on...Ch. 1.3 - If you roll a 1 -m-diameter wheel forward 30 cm...Ch. 1.3 - Copy and complete the following table of function...Ch. 1.3 - Copy and complete the following table of function...Ch. 1.3 - In Exercises 7–12, one of sin x, cos x, and tan x...Ch. 1.3 - In Exercises 7–12, one of sin x, cos x, and tan x...Ch. 1.3 - In Exercises 7–12, one of sin x, cos x, and tan x...Ch. 1.3 - Prob. 10ECh. 1.3 - Prob. 11ECh. 1.3 - In Exercises 7–12, one of sin x, cos x, and tan x...Ch. 1.3 - Graph the functions in Exercises 13–22. What is...Ch. 1.3 - Graph the functions in Exercises 13–22. What is...Ch. 1.3 - Graph the functions in Exercises 13–22. What is...Ch. 1.3 - Graph the functions in Exercises 13–22. What is...Ch. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Graph y = cos x and y = sec x together for ....Ch. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prob. 30ECh. 1.3 - Use the addition formulas to derive the identities...Ch. 1.3 - Use the addition formulas to derive the identities...Ch. 1.3 - Use the addition formulas to derive the identities...Ch. 1.3 - Use the addition formulas to derive the identities...Ch. 1.3 - Use the addition formulas to derive the identities...Ch. 1.3 - Prob. 36ECh. 1.3 - What happens if you take B = A in the...Ch. 1.3 - Prob. 38ECh. 1.3 - In Exercises 39–42, express the given quantity in...Ch. 1.3 - In Exercises 39–42, express the given quantity in...Ch. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - Prob. 43ECh. 1.3 - Evaluate as .
Ch. 1.3 - Prob. 45ECh. 1.3 - Evaluate .
Ch. 1.3 - Using the Half-Angle Formulas
Find the function...Ch. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - Prob. 50ECh. 1.3 - Prob. 51ECh. 1.3 - Prob. 52ECh. 1.3 - Solving Trigonometric Equations
For Exercise...Ch. 1.3 - Solving Trigonometric Equations
For Exercise...Ch. 1.3 - Prob. 55ECh. 1.3 - Prob. 56ECh. 1.3 - Apply the law of cosines to the triangle in the...Ch. 1.3 - Prob. 58ECh. 1.3 - Prob. 59ECh. 1.3 - Prob. 60ECh. 1.3 - The law of sines The law of sines says that if a,...Ch. 1.3 - Prob. 62ECh. 1.3 - A triangle has side c = 2 and angles and .Find...Ch. 1.3 - Consider the length h of the perpendicular from...Ch. 1.3 - Refer to the given figure. Write the radius r of...Ch. 1.3 - Prob. 66ECh. 1.3 - Prob. 67ECh. 1.3 - Prob. 68ECh. 1.3 - Prob. 69ECh. 1.3 - Prob. 70ECh. 1.4 - Choosing a Viewing Window
In Exercises 1–4, use...Ch. 1.4 - Choosing a Viewing Window
In Exercises 1–4, use...Ch. 1.4 - Choosing a Viewing Window
In Exercises 1–4, use...Ch. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Finding a Viewing Window
In Exercises 5–30, find...Ch. 1.4 - Finding a Viewing Window
In Exercises 5–30, find...Ch. 1.4 - Finding a Viewing Window
In Exercises 5–30, find...Ch. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Finding a Viewing Window
In Exercises 5–30, find...Ch. 1.4 - Prob. 23ECh. 1.4 - Finding a Viewing Window
In Exercises 5–30, find...Ch. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Use graphing software to graph the functions...Ch. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1.4 - Prob. 35ECh. 1.4 - Use graphing software to graph the functions...Ch. 1 - Prob. 1GYRCh. 1 - What is the graph of a real-valued function of a...Ch. 1 - What is a piecewise-defined function? Give...Ch. 1 - What are the important types of functions...Ch. 1 - What is meant by an increasing function? A...Ch. 1 - What is an even function? An odd function? What...Ch. 1 - If f and g are real-valued functions, how are the...Ch. 1 - When is it possible to compose one function with...Ch. 1 - How do you change the equation y = f(x) to shift...Ch. 1 - Prob. 10GYRCh. 1 - Prob. 11GYRCh. 1 - Prob. 12GYRCh. 1 - Prob. 13GYRCh. 1 - Prob. 14GYRCh. 1 - Prob. 15GYRCh. 1 - Name three issues that arise when functions are...Ch. 1 - Express the area and circumference of a circle as...Ch. 1 - Prob. 2PECh. 1 - A point P in the first quadrant lies on the...Ch. 1 - Prob. 4PECh. 1 - In Exercises 5–8, determine whether the graph of...Ch. 1 - Prob. 6PECh. 1 - Prob. 7PECh. 1 - Prob. 8PECh. 1 - Prob. 9PECh. 1 - Prob. 10PECh. 1 - Prob. 11PECh. 1 - Prob. 12PECh. 1 - Prob. 13PECh. 1 - Prob. 14PECh. 1 - Prob. 15PECh. 1 - In Exercises 9–16, determine whether the function...Ch. 1 - Prob. 17PECh. 1 - Prob. 18PECh. 1 - In Exercises 19–32, find the (a) domain and (b)...Ch. 1 - Prob. 20PECh. 1 - Prob. 21PECh. 1 - In Exercises 19–32, find the (a) domain and (b)...Ch. 1 - Prob. 23PECh. 1 - Prob. 24PECh. 1 - Prob. 25PECh. 1 - Prob. 26PECh. 1 - Prob. 27PECh. 1 - Prob. 28PECh. 1 - Prob. 29PECh. 1 - Prob. 30PECh. 1 - Prob. 31PECh. 1 - Prob. 32PECh. 1 - State whether each function is increasing,...Ch. 1 - Prob. 34PECh. 1 - Prob. 35PECh. 1 - Prob. 36PECh. 1 - In Exercises 37 and 38, write a piecewise formula...Ch. 1 - In Exercises 37 and 38, write a piecewise formula...Ch. 1 - Prob. 39PECh. 1 - Prob. 40PECh. 1 - In Exercises 41 and 42, (a) write formulas for f ∘...Ch. 1 - Prob. 42PECh. 1 - For Exercises 43 and 44, sketch the graphs of f...Ch. 1 - Prob. 44PECh. 1 - Prob. 45PECh. 1 - Prob. 46PECh. 1 - Prob. 47PECh. 1 - Prob. 48PECh. 1 - Prob. 49PECh. 1 - Prob. 50PECh. 1 - Prob. 51PECh. 1 - Prob. 52PECh. 1 - Suppose the graph of g is given. Write equations...Ch. 1 - Prob. 54PECh. 1 - In Exercises 55–58, graph each function, not by...Ch. 1 - In Exercises 55–58, graph each function, not by...Ch. 1 - Prob. 57PECh. 1 - Prob. 58PECh. 1 - Prob. 59PECh. 1 - Prob. 60PECh. 1 - Prob. 61PECh. 1 - Prob. 62PECh. 1 - Prob. 63PECh. 1 - Prob. 64PECh. 1 - Prob. 65PECh. 1 - Prob. 66PECh. 1 - Prob. 67PECh. 1 - In Exercises 65–68, ABC is a right triangle with...Ch. 1 - Height of a pole Two wires stretch from the top T...Ch. 1 - Prob. 70PECh. 1 - Prob. 71PECh. 1 - Prob. 72PECh. 1 - Prob. 1AAECh. 1 - Prob. 2AAECh. 1 - Prob. 3AAECh. 1 - If g(x) is an odd function defined for all values...Ch. 1 -
Graph the equation |x| + |y| = 1 + x.
Ch. 1 -
Graph the equation y + |y| = x + |x|.
Ch. 1 - Prob. 7AAECh. 1 - Prob. 8AAECh. 1 - Prob. 9AAECh. 1 - Prob. 10AAECh. 1 - Show that if f is both even and odd, then f(x) = 0...Ch. 1 - Prob. 12AAECh. 1 - Prob. 13AAECh. 1 - Prob. 14AAECh. 1 -
An object’s center of mass moves at a constant...Ch. 1 - Prob. 16AAECh. 1 - Consider the quarter-circle of radius 1 and right...Ch. 1 - Let f(x) = ax + b and g(x) = cx + d. What...
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