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Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
4th Edition
ISBN: 9780134686974
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Question
Chapter 13.3, Problem 68AYU
To determine
To find: The numbers at which is continuous.
Expert Solution & Answer
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Students have asked these similar questions
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.
A
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(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
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
Need Help? Read It
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Chapter 13 Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Ch. 13.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 13.1 - If f( x )={ xifx0 1ifx0 what is f( 0 ) ?...Ch. 13.1 - 3. The limit of a function f (x) as x approaches c...Ch. 13.1 - If a function f has no limit as x approaches c,...Ch. 13.1 - True or False may be described by saving that the...Ch. 13.1 - True or False lim xc f( x ) exists and equals some...Ch. 13.1 -
Ch. 13.1 - lim x3 ( 2 x 2 +1 )Ch. 13.1 -
Ch. 13.1 - lim x0 2x x 2 +4
Ch. 13.1 - lim x4 x 2 4x x4Ch. 13.1 -
Ch. 13.1 -
Ch. 13.1 - Prob. 14AYUCh. 13.1 - , x in radians
Ch. 13.1 - lim x0 tanx x , x in radiansCh. 13.1 -
Ch. 13.1 - In Problems 17-22, use the graph shown to...Ch. 13.1 - In Problems 17-22, use the graph shown to...Ch. 13.1 - In Problems 17-22, use the graph shown to...Ch. 13.1 - In Problems 17-22, use the graph shown to...Ch. 13.1 - In Problems 17-22, use the graph shown to...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 23-42, graph each function. Use the...Ch. 13.1 - In Problems 43-48, use a graphing utility to find...Ch. 13.1 - In Problems 43-48, use a graphing utility to find...Ch. 13.1 - In Problems 43-48, use a graphing utility to find...Ch. 13.1 - In Problems 43-48, use a graphing utility to find...Ch. 13.1 - In Problems 43-48, use a graphing utility to find...Ch. 13.1 - In Problems 43-48, use a graphing utility to find...Ch. 13.1 - Problems 49 52 are based on material learned...Ch. 13.1 - Find the center, foci, and vertices of the ellipse...Ch. 13.1 - Problems 49 – 52 are based on material learned...Ch. 13.1 - Problems 49 – 52 are based on material learned...Ch. 13.2 - The limit of the product of two functions equals...Ch. 13.2 - limxcb= ______.Ch. 13.2 - 3.
(a) x (b) c (c) cx (d) x/c
Ch. 13.2 - True or False The limit of a polynomial function...Ch. 13.2 - True or False The limit of a rational function at...Ch. 13.2 - True or false The limit of a quotient equals the...Ch. 13.2 - In Problems 7- 42, find each limit algebraically....Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7 – 42, find each limit...Ch. 13.2 - In Problems 7 42, find each limit algebraically....Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7 – 42, find each limit...Ch. 13.2 - In Problem 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7- 42, find each limit...Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 7-42, find each limit algebraically....Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In Problems 43-52, find the limit as x approaches...Ch. 13.2 - In problems 53-56, use the properties of limits...Ch. 13.2 - In problems 53-56, use the properties of limits...Ch. 13.2 - In problems 53-56, use the properties of limits...Ch. 13.2 - In problems 53-56, use the properties of limits...Ch. 13.2 - Graph the function f(x)=x3+x2+1.Ch. 13.2 - Problem 57-60 are based on material learned...Ch. 13.2 - Problem 57-60 are based on material learned...Ch. 13.2 - Problem 57-60 are based on material learned...Ch. 13.3 - For the function f( x )={ x 2 ifx0 x+1if0x2...Ch. 13.3 - What are the domain and range of f( x )=lnx ?Ch. 13.3 - Prob. 3AYUCh. 13.3 - Prob. 4AYUCh. 13.3 - Prob. 5AYUCh. 13.3 - Prob. 6AYUCh. 13.3 - Prob. 7AYUCh. 13.3 - Prob. 8AYUCh. 13.3 - Prob. 9AYUCh. 13.3 - Prob. 10AYUCh. 13.3 - Prob. 11AYUCh. 13.3 - Prob. 12AYUCh. 13.3 - Prob. 13AYUCh. 13.3 - Prob. 14AYUCh. 13.3 - Prob. 15AYUCh. 13.3 - Prob. 16AYUCh. 13.3 - Prob. 17AYUCh. 13.3 - Prob. 18AYUCh. 13.3 - Prob. 19AYUCh. 13.3 - Prob. 20AYUCh. 13.3 - Prob. 21AYUCh. 13.3 - Prob. 22AYUCh. 13.3 - Prob. 23AYUCh. 13.3 - Prob. 24AYUCh. 13.3 - Prob. 25AYUCh. 13.3 - Prob. 26AYUCh. 13.3 - Prob. 27AYUCh. 13.3 - Prob. 28AYUCh. 13.3 - Prob. 29AYUCh. 13.3 - Prob. 30AYUCh. 13.3 - Prob. 31AYUCh. 13.3 - Prob. 32AYUCh. 13.3 - Prob. 33AYUCh. 13.3 - Prob. 34AYUCh. 13.3 - Prob. 35AYUCh. 13.3 - Prob. 36AYUCh. 13.3 - Prob. 37AYUCh. 13.3 - Prob. 38AYUCh. 13.3 - Prob. 39AYUCh. 13.3 - Prob. 40AYUCh. 13.3 - Prob. 41AYUCh. 13.3 - Prob. 42AYUCh. 13.3 - Prob. 43AYUCh. 13.3 - Prob. 44AYUCh. 13.3 - Prob. 45AYUCh. 13.3 - Prob. 46AYUCh. 13.3 - Prob. 47AYUCh. 13.3 - Prob. 48AYUCh. 13.3 - Prob. 49AYUCh. 13.3 - Prob. 50AYUCh. 13.3 - Prob. 51AYUCh. 13.3 - Prob. 52AYUCh. 13.3 - Prob. 53AYUCh. 13.3 - Prob. 54AYUCh. 13.3 - Prob. 55AYUCh. 13.3 - Prob. 56AYUCh. 13.3 - Prob. 57AYUCh. 13.3 - Prob. 58AYUCh. 13.3 - Prob. 59AYUCh. 13.3 - Prob. 60AYUCh. 13.3 - Prob. 61AYUCh. 13.3 - Prob. 62AYUCh. 13.3 - Prob. 63AYUCh. 13.3 - Prob. 64AYUCh. 13.3 - Prob. 65AYUCh. 13.3 - Prob. 66AYUCh. 13.3 - Prob. 67AYUCh. 13.3 - Prob. 68AYUCh. 13.3 - Prob. 69AYUCh. 13.3 - Prob. 70AYUCh. 13.3 - Prob. 71AYUCh. 13.3 - Prob. 72AYUCh. 13.3 - Prob. 73AYUCh. 13.3 - Prob. 74AYUCh. 13.3 - Prob. 75AYUCh. 13.3 - Prob. 76AYUCh. 13.3 - Prob. 77AYUCh. 13.3 - Prob. 78AYUCh. 13.3 - Prob. 79AYUCh. 13.3 - Prob. 80AYUCh. 13.3 - Prob. 81AYUCh. 13.3 - Prob. 82AYUCh. 13.3 - Prob. 83AYUCh. 13.3 - Prob. 84AYUCh. 13.3 - Prob. 85AYUCh. 13.3 - Prob. 86AYUCh. 13.3 - Prob. 87AYUCh. 13.3 - Prob. 88AYUCh. 13.3 - Prob. 89AYUCh. 13.3 - Prob. 90AYUCh. 13.3 - Prob. 91AYUCh. 13.3 - Prob. 92AYUCh. 13.3 - Prob. 93AYUCh. 13.3 - Prob. 94AYUCh. 13.4 - Prob. 1AYUCh. 13.4 - Prob. 2AYUCh. 13.4 - Prob. 3AYUCh. 13.4 - Prob. 4AYUCh. 13.4 - Prob. 5AYUCh. 13.4 - Prob. 6AYUCh. 13.4 - Prob. 7AYUCh. 13.4 - Prob. 8AYUCh. 13.4 - Prob. 9AYUCh. 13.4 - Prob. 10AYUCh. 13.4 - Prob. 11AYUCh. 13.4 - Prob. 12AYUCh. 13.4 - Prob. 13AYUCh. 13.4 - Prob. 14AYUCh. 13.4 - Prob. 15AYUCh. 13.4 - Prob. 16AYUCh. 13.4 - Prob. 17AYUCh. 13.4 - Prob. 18AYUCh. 13.4 - Prob. 19AYUCh. 13.4 - Prob. 20AYUCh. 13.4 - Prob. 21AYUCh. 13.4 - Prob. 22AYUCh. 13.4 - Prob. 23AYUCh. 13.4 - Prob. 24AYUCh. 13.4 - Prob. 25AYUCh. 13.4 - Prob. 26AYUCh. 13.4 - Prob. 27AYUCh. 13.4 - Prob. 28AYUCh. 13.4 - Prob. 29AYUCh. 13.4 - Prob. 30AYUCh. 13.4 - Prob. 31AYUCh. 13.4 - Prob. 32AYUCh. 13.4 - Prob. 33AYUCh. 13.4 - Prob. 34AYUCh. 13.4 - Prob. 35AYUCh. 13.4 - Prob. 36AYUCh. 13.4 - Prob. 37AYUCh. 13.4 - Prob. 38AYUCh. 13.4 - Prob. 39AYUCh. 13.4 - Prob. 40AYUCh. 13.4 - Prob. 41AYUCh. 13.4 - Prob. 42AYUCh. 13.4 - Prob. 43AYUCh. 13.4 - Prob. 44AYUCh. 13.4 - Prob. 45AYUCh. 13.4 - Instantaneous Rate of Change The volume V of a...Ch. 13.4 - instantaneous Velocity of a Ball In physics it is...Ch. 13.4 - Prob. 48AYUCh. 13.4 - Prob. 49AYUCh. 13.4 - Prob. 50AYUCh. 13.4 - Prob. 51AYUCh. 13.4 - Prob. 52AYUCh. 13.4 - Prob. 53AYUCh. 13.4 - Prob. 54AYUCh. 13.5 - The formula for the area A of a rectangle of...Ch. 13.5 - ______.(pp.828-831)
Ch. 13.5 - Prob. 3AYUCh. 13.5 - Prob. 4AYUCh. 13.5 - Prob. 5AYUCh. 13.5 - Prob. 6AYUCh. 13.5 - Prob. 7AYUCh. 13.5 - Prob. 8AYUCh. 13.5 - Prob. 9AYUCh. 13.5 - Prob. 10AYUCh. 13.5 - Prob. 11AYUCh. 13.5 - Prob. 12AYUCh. 13.5 - Prob. 13AYUCh. 13.5 - Prob. 14AYUCh. 13.5 - Prob. 15AYUCh. 13.5 - Prob. 16AYUCh. 13.5 - Prob. 17AYUCh. 13.5 - Prob. 18AYUCh. 13.5 - Prob. 19AYUCh. 13.5 - Prob. 20AYUCh. 13.5 - Prob. 21AYUCh. 13.5 - Prob. 22AYUCh. 13.5 - Prob. 23AYUCh. 13.5 - Prob. 24AYUCh. 13.5 - Prob. 25AYUCh. 13.5 - Prob. 26AYUCh. 13.5 - Prob. 27AYUCh. 13.5 - Prob. 28AYUCh. 13.5 - Prob. 29AYUCh. 13.5 - Prob. 30AYUCh. 13.5 - Prob. 31AYUCh. 13.5 - Prob. 32AYUCh. 13.5 - Prob. 33AYUCh. 13.5 - Prob. 34AYUCh. 13.5 - Prob. 35AYUCh. 13.5 - Prob. 36AYUCh. 13 - In Problems 111, find the limit. limx2(3x22x+1)Ch. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - In Problems 1– 11, find each limit...Ch. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Prob. 25RECh. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - Prob. 30RECh. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Prob. 35RECh. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - Instantaneous Velocity of a Ball In physics it is...Ch. 13 - Prob. 39RECh. 13 - Prob. 40RECh. 13 - Prob. 41RECh. 13 - Prob. 42RECh. 13 - Prob. 43RECh. 13 - Prob. 44RECh. 13 - Prob. 1CTCh. 13 - Prob. 2CTCh. 13 - Prob. 3CTCh. 13 - Prob. 4CTCh. 13 - Prob. 5CTCh. 13 - Prob. 6CTCh. 13 - Prob. 7CTCh. 13 - Prob. 8CTCh. 13 - Prob. 9CTCh. 13 - Prob. 10CTCh. 13 - Prob. 11CTCh. 13 - Prob. 12CTCh. 13 - Prob. 13CTCh. 13 - Prob. 14CTCh. 13 - Prob. 15CTCh. 13 - Prob. 16CTCh. 13 - Prob. 17CT
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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…arrow_forward4. [-/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 Need Help? Read It ' and Es is decreased by a factor of aboutarrow_forward6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4arrow_forward
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