Calculus: An Applied Approach (Providence College: MTH 109)
9th Edition
ISBN: 9781285142616
Author: Ron Larson
Publisher: CENGAGE C
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Chapter 8.4, Problem 4CP
(a)
To determine
To calculate: The derivative of the trigonometric function
(b)
To determine
To calculate: The derivative of the trigonometric function
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Chapter 8 Solutions
Calculus: An Applied Approach (Providence College: MTH 109)
Ch. 8.1 - For each angle, find a coterminal angle such that...Ch. 8.1 - Prob. 2CPCh. 8.1 - Prob. 3CPCh. 8.1 - Prob. 4CPCh. 8.1 - Prob. 1SWUCh. 8.1 - Prob. 2SWUCh. 8.1 - Prob. 3SWUCh. 8.1 - Prob. 4SWUCh. 8.1 - Prob. 5SWUCh. 8.1 - Prob. 6SWU
Ch. 8.1 - Prob. 7SWUCh. 8.1 - Prob. 8SWUCh. 8.1 - Prob. 9SWUCh. 8.1 - Prob. 10SWUCh. 8.1 - Prob. 1ECh. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Prob. 3ECh. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Finding Conterminal Angles In Exercise 7-10,...Ch. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10ECh. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Height A person 6 feet tall standing 16 feet from...Ch. 8.1 - Length A guy wire is stretched from a broadcasting...Ch. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Arc Length In Exercises 47-50, use the following...Ch. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - How do you see it? Determine which angles in the...Ch. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.2 - Let (3,1) be a point on the terminal side of , as...Ch. 8.2 - Prob. 2CPCh. 8.2 - Prob. 3CPCh. 8.2 - Prob. 4CPCh. 8.2 - Prob. 5CPCh. 8.2 - Prob. 6CPCh. 8.2 - Prob. 7CPCh. 8.2 - Prob. 1SWUCh. 8.2 - Prob. 2SWUCh. 8.2 - Prob. 3SWUCh. 8.2 - Prob. 4SWUCh. 8.2 - Prob. 5SWUCh. 8.2 - Prob. 6SWUCh. 8.2 - Prob. 7SWUCh. 8.2 - Prob. 8SWUCh. 8.2 - Prob. 9SWUCh. 8.2 - Prob. 10SWUCh. 8.2 - Prob. 11SWUCh. 8.2 - Prob. 12SWUCh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Prob. 5ECh. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Prob. 59ECh. 8.2 - Prob. 60ECh. 8.2 - Prob. 61ECh. 8.2 - Prob. 62ECh. 8.2 - Prob. 63ECh. 8.2 - Prob. 64ECh. 8.2 - Prob. 65ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.2 - Prob. 68ECh. 8.2 - Prob. 69ECh. 8.2 - Prob. 70ECh. 8.2 - Length A 20-foot ladder leaning against the side...Ch. 8.2 - Width of a River A biologist wants to know the...Ch. 8.2 - Distance An airplane flying at an altitude of 6...Ch. 8.2 - Skateboard Ramp A skateboard ramp with a height of...Ch. 8.2 - Height A 25-meter line is used to tether a...Ch. 8.2 - Empire State Building You are standing 45 meters...Ch. 8.2 - Prob. 77ECh. 8.2 - Prob. 78ECh. 8.2 - Height of a Mountain In traveling across flat...Ch. 8.2 - Prob. 80ECh. 8.2 - Medicine The temperature T (in degrees Fahrenheit)...Ch. 8.2 - Prob. 82ECh. 8.2 - Prob. 83ECh. 8.2 - Prob. 84ECh. 8.2 - Prob. 85ECh. 8.2 - Prob. 86ECh. 8.2 - Prob. 87ECh. 8.2 - Prob. 88ECh. 8.3 - Prob. 1CPCh. 8.3 - Prob. 2CPCh. 8.3 - Prob. 3CPCh. 8.3 - Prob. 4CPCh. 8.3 - Prob. 5CPCh. 8.3 - Prob. 6CPCh. 8.3 - Prob. 1SWUCh. 8.3 - Prob. 2SWUCh. 8.3 - Prob. 3SWUCh. 8.3 - Prob. 4SWUCh. 8.3 - Prob. 5SWUCh. 8.3 - Prob. 6SWUCh. 8.3 - Prob. 7SWUCh. 8.3 - Prob. 8SWUCh. 8.3 - Prob. 9SWUCh. 8.3 - Prob. 10SWUCh. 8.3 - Prob. 11SWUCh. 8.3 - Prob. 12SWUCh. 8.3 - Prob. 13SWUCh. 8.3 - Prob. 14SWUCh. 8.3 - Prob. 15SWUCh. 8.3 - Prob. 16SWUCh. 8.3 - Prob. 17SWUCh. 8.3 - Prob. 18SWUCh. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - Prob. 39ECh. 8.3 - Prob. 40ECh. 8.3 - Prob. 41ECh. 8.3 - Prob. 42ECh. 8.3 - Prob. 43ECh. 8.3 - Prob. 44ECh. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 51ECh. 8.3 - Prob. 52ECh. 8.3 - Prob. 53ECh. 8.3 - Prob. 54ECh. 8.3 - Prob. 55ECh. 8.3 - Prob. 56ECh. 8.3 - Prob. 57ECh. 8.3 - Prob. 58ECh. 8.3 - Prob. 59ECh. 8.3 - Prob. 60ECh. 8.3 - Prob. 61ECh. 8.3 - Prob. 62ECh. 8.3 - Graphical Reasoning In Exercises 63-66, find a and...Ch. 8.3 - Prob. 64ECh. 8.3 - Graphical Reasoning In Exercises 63-66, find a and...Ch. 8.3 - Graphical Reasoning In Exercises 63-66, find a and...Ch. 8.3 - Prob. 67ECh. 8.3 - Prob. 68ECh. 8.3 - Prob. 69ECh. 8.3 - Prob. 70ECh. 8.3 - Prob. 71ECh. 8.3 - Prob. 72ECh. 8.3 - Prob. 73ECh. 8.3 - Biology: Predator-Prey Cycle The population P of a...Ch. 8.3 - Music When tuning a piano, a technician strikes a...Ch. 8.3 - Health The function P=10020cos5t3 approximates the...Ch. 8.3 - Prob. 77ECh. 8.3 - Prob. 78ECh. 8.3 - Prob. 79ECh. 8.3 - Prob. 80ECh. 8.3 - Prob. 81ECh. 8.3 - Prob. 82ECh. 8.3 - Prob. 83ECh. 8.3 - HOW DO YOU SEE IT? The normal monthly high...Ch. 8.3 - True or False? In Exercises 8588, determine...Ch. 8.3 - Prob. 86ECh. 8.3 - Prob. 87ECh. 8.3 - Prob. 88ECh. 8.3 - Prob. 1QYCh. 8.3 - Prob. 2QYCh. 8.3 - Prob. 3QYCh. 8.3 - Prob. 4QYCh. 8.3 - Prob. 5QYCh. 8.3 - Prob. 6QYCh. 8.3 - Prob. 7QYCh. 8.3 - Prob. 8QYCh. 8.3 - Prob. 9QYCh. 8.3 - Prob. 10QYCh. 8.3 - Prob. 11QYCh. 8.3 - Prob. 12QYCh. 8.3 - Prob. 13QYCh. 8.3 - In Exercises 914, evaluate the trigonometric...Ch. 8.3 - Prob. 15QYCh. 8.3 - Prob. 16QYCh. 8.3 - In Exercises 15-17, solve the equation for ....Ch. 8.3 - Prob. 18QYCh. 8.3 - Prob. 19QYCh. 8.3 - Prob. 20QYCh. 8.3 - A map maker needs to determine the distance d...Ch. 8.3 - Prob. 22QYCh. 8.3 - Prob. 23QYCh. 8.3 - Prob. 24QYCh. 8.3 - Prob. 25QYCh. 8.4 - Differentiate each function. a. y=cos4x b....Ch. 8.4 - Prob. 2CPCh. 8.4 - Prob. 3CPCh. 8.4 - Prob. 4CPCh. 8.4 - Prob. 5CPCh. 8.4 - Prob. 6CPCh. 8.4 - Prob. 7CPCh. 8.4 - Prob. 8CPCh. 8.4 - Prob. 9CPCh. 8.4 - Prob. 1SWUCh. 8.4 - Prob. 2SWUCh. 8.4 - Prob. 3SWUCh. 8.4 - Prob. 4SWUCh. 8.4 - Prob. 5SWUCh. 8.4 - Prob. 6SWUCh. 8.4 - Prob. 7SWUCh. 8.4 - Prob. 8SWUCh. 8.4 - In Exercises 7-10, solve the equation for x....Ch. 8.4 - Prob. 10SWUCh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Prob. 31ECh. 8.4 - Prob. 32ECh. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Prob. 36ECh. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8.4 - Prob. 39ECh. 8.4 - Prob. 40ECh. 8.4 - Slope of a Tangent Line In Exercises 41 and 42,...Ch. 8.4 - Prob. 42ECh. 8.4 - Prob. 43ECh. 8.4 - Prob. 44ECh. 8.4 - Prob. 45ECh. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Prob. 49ECh. 8.4 - Prob. 50ECh. 8.4 - Prob. 51ECh. 8.4 - Prob. 52ECh. 8.4 - Prob. 53ECh. 8.4 - Prob. 54ECh. 8.4 - Prob. 55ECh. 8.4 - Prob. 56ECh. 8.4 - Prob. 57ECh. 8.4 - Prob. 58ECh. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Prob. 60ECh. 8.4 - Prob. 61ECh. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Prob. 63ECh. 8.4 - Prob. 64ECh. 8.4 - Prob. 65ECh. 8.4 - Prob. 66ECh. 8.4 - Prob. 67ECh. 8.4 - Prob. 68ECh. 8.4 - Transportation Workers The number W (in thousands)...Ch. 8.4 - Employment The number W (in thousands) of golf...Ch. 8.4 - Biology Plants do not grow at constant rates...Ch. 8.4 - Tides Throughout the day, the depth of water D (in...Ch. 8.4 - Prob. 73ECh. 8.4 - HOW DO YOU SEE IT? The graph shows the height h...Ch. 8.4 - Analyzing a Function In Exercises 75-80, use a...Ch. 8.4 - Prob. 76ECh. 8.4 - Prob. 77ECh. 8.4 - Prob. 78ECh. 8.4 - Prob. 79ECh. 8.4 - Prob. 80ECh. 8.4 - Prob. 81ECh. 8.4 - Prob. 82ECh. 8.4 - Prob. 83ECh. 8.4 - Prob. 84ECh. 8.5 - Find 5sinxdx.Ch. 8.5 - Prob. 2CPCh. 8.5 - Prob. 3CPCh. 8.5 - Prob. 4CPCh. 8.5 - Prob. 5CPCh. 8.5 - Prob. 6CPCh. 8.5 - Prob. 7CPCh. 8.5 - Prob. 8CPCh. 8.5 - Prob. 9CPCh. 8.5 - Prob. 1SWUCh. 8.5 - Prob. 2SWUCh. 8.5 - Prob. 3SWUCh. 8.5 - Prob. 4SWUCh. 8.5 - Prob. 5SWUCh. 8.5 - Prob. 6SWUCh. 8.5 - Prob. 7SWUCh. 8.5 - Prob. 8SWUCh. 8.5 - Prob. 9SWUCh. 8.5 - Prob. 10SWUCh. 8.5 - Prob. 11SWUCh. 8.5 - Prob. 12SWUCh. 8.5 - Prob. 13SWUCh. 8.5 - Prob. 14SWUCh. 8.5 - In Exercises 9-16, simplify the expression using...Ch. 8.5 - Prob. 16SWUCh. 8.5 - Prob. 17SWUCh. 8.5 - Prob. 18SWUCh. 8.5 - Prob. 19SWUCh. 8.5 - Prob. 20SWUCh. 8.5 - Prob. 1ECh. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Prob. 5ECh. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Prob. 9ECh. 8.5 - Prob. 10ECh. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Integrating a Trigonometric Function In Exercises...Ch. 8.5 - Prob. 14ECh. 8.5 - Prob. 15ECh. 8.5 - Prob. 16ECh. 8.5 - Prob. 17ECh. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.5 - Prob. 21ECh. 8.5 - Prob. 22ECh. 8.5 - Integrating a Trigonometric Function In Exercises...Ch. 8.5 - Prob. 24ECh. 8.5 - Prob. 25ECh. 8.5 - Prob. 26ECh. 8.5 - Prob. 27ECh. 8.5 - Prob. 28ECh. 8.5 - Prob. 29ECh. 8.5 - Prob. 30ECh. 8.5 - Prob. 31ECh. 8.5 - Prob. 32ECh. 8.5 - Prob. 33ECh. 8.5 - Integration by Parts In Exercises 33-38, use...Ch. 8.5 - Prob. 35ECh. 8.5 - Prob. 36ECh. 8.5 - Prob. 37ECh. 8.5 - Prob. 38ECh. 8.5 - Prob. 39ECh. 8.5 - Prob. 40ECh. 8.5 - Prob. 41ECh. 8.5 - Prob. 42ECh. 8.5 - Prob. 43ECh. 8.5 - Prob. 44ECh. 8.5 - Prob. 45ECh. 8.5 - Prob. 46ECh. 8.5 - Prob. 47ECh. 8.5 - Prob. 48ECh. 8.5 - Prob. 49ECh. 8.5 - Prob. 50ECh. 8.5 - Prob. 51ECh. 8.5 - Prob. 52ECh. 8.5 - Prob. 53ECh. 8.5 - Finding the Area of a Region In Exercises 53-56,...Ch. 8.5 - Prob. 55ECh. 8.5 - Prob. 56ECh. 8.5 - Prob. 57ECh. 8.5 - Prob. 58ECh. 8.5 - Prob. 59ECh. 8.5 - Prob. 60ECh. 8.5 - Cost The temperature T (in degrees Fahrenheit) in...Ch. 8.5 - Water Supply The flow rate R (in thousands of...Ch. 8.5 - Prob. 63ECh. 8.5 - Prob. 64ECh. 8.5 - Prob. 67ECh. 8.5 - Prob. 68ECh. 8 - Finding Coterminal Angles In Exercises 1 4,...Ch. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Height A 16-foot ladder leans against the side of...Ch. 8 - Height A person 6 feet tall walks away from a...Ch. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Solving a Right Triangle In Exercises 4144, solve...Ch. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Solving a Trigonometric Equation In Exercises...Ch. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Height The length of the shadow of a tree is 125...Ch. 8 - Length A guy wire runs from the ground to a cell...Ch. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - Prob. 61RECh. 8 - Prob. 62RECh. 8 - Prob. 63RECh. 8 - Prob. 64RECh. 8 - Prob. 65RECh. 8 - Prob. 66RECh. 8 - Differentiating trigonometric Functions In...Ch. 8 - Prob. 68RECh. 8 - Prob. 69RECh. 8 - Prob. 70RECh. 8 - Prob. 71RECh. 8 - Prob. 72RECh. 8 - Prob. 73RECh. 8 - Prob. 74RECh. 8 - Prob. 75RECh. 8 - Prob. 76RECh. 8 - Prob. 77RECh. 8 - Prob. 78RECh. 8 - Prob. 79RECh. 8 - Prob. 80RECh. 8 - Prob. 81RECh. 8 - Prob. 82RECh. 8 - Prob. 83RECh. 8 - Prob. 84RECh. 8 - Prob. 85RECh. 8 - Prob. 86RECh. 8 - Prob. 87RECh. 8 - Prob. 88RECh. 8 - Prob. 89RECh. 8 - Prob. 90RECh. 8 - Finding Relative Extrema In Exercises 91-96, find...Ch. 8 - Finding Relative Extrema In Exercises 91-96, find...Ch. 8 - Prob. 93RECh. 8 - Prob. 94RECh. 8 - Prob. 95RECh. 8 - Prob. 96RECh. 8 - Prob. 97RECh. 8 - Prob. 98RECh. 8 - Prob. 99RECh. 8 - Prob. 100RECh. 8 - Integrating a Trigonometric Function In Exercises...Ch. 8 - Prob. 102RECh. 8 - Prob. 103RECh. 8 - Prob. 104RECh. 8 - Prob. 105RECh. 8 - Prob. 106RECh. 8 - Prob. 107RECh. 8 - Integrating a Trigonometric Function In Exercises...Ch. 8 - Prob. 109RECh. 8 - Prob. 110RECh. 8 - Prob. 111RECh. 8 - Prob. 112RECh. 8 - Prob. 113RECh. 8 - Prob. 114RECh. 8 - Evaluating a Definite Integral In Exercises...Ch. 8 - Prob. 116RECh. 8 - Prob. 117RECh. 8 - Prob. 118RECh. 8 - Prob. 119RECh. 8 - Prob. 120RECh. 8 - Prob. 121RECh. 8 - Prob. 122RECh. 8 - Prob. 123RECh. 8 - Health For a person at rest, the velocity v (in...Ch. 8 - Prob. 125RECh. 8 - Prob. 126RECh. 8 - Prob. 1TYSCh. 8 - Prob. 2TYSCh. 8 - Prob. 3TYSCh. 8 - Prob. 4TYSCh. 8 - Prob. 5TYSCh. 8 - Prob. 6TYSCh. 8 - At a distance of 19 feet from the base, the angle...Ch. 8 - Prob. 8TYSCh. 8 - Prob. 9TYSCh. 8 - Prob. 10TYSCh. 8 - Prob. 11TYSCh. 8 - Prob. 12TYSCh. 8 - Prob. 13TYSCh. 8 - Prob. 14TYSCh. 8 - Prob. 15TYSCh. 8 - Prob. 16TYSCh. 8 - Prob. 17TYSCh. 8 - Prob. 18TYSCh. 8 - Prob. 19TYSCh. 8 - Prob. 20TYSCh. 8 - Prob. 21TYSCh. 8 - Prob. 22TYSCh. 8 - Prob. 23TYSCh. 8 - Prob. 24TYS
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- let θ = 17π over 12 Part A: Determine tan θ using the sum formula. Show all necessary work in the calculation.Part B: Determine cos θ using the difference formula. Show all necessary work in the calculation.arrow_forwardCalculus lll May I please have an explanation about how to calculate the derivative of the surface (the dS) on the surface integral, and then explain the essentials of the surface integral?arrow_forwardУ1 = e is a solution to the differential equation xy" — (x+1)y' + y = 0. Use reduction of order to find the solution y(x) corresponding to the initial data y(1) = 1, y′ (1) = 0. Then sin(y(2.89)) is -0.381 0.270 -0.401 0.456 0.952 0.981 -0.152 0.942arrow_forward
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- Thumbi Irrigation Scheme in Mzimba district is under threat of flooding. In order to mitigate against the problem, authorities have decided to construct a flood protection bund (Dyke). Figure 1 is a cross section of a 300m long proposed dyke; together with its foundation (key). Survey data for the proposed site of the dyke are presented in Table 1. Table 2 provides swelling and shrinkage factors for the fill material that has been proposed. The dyke dimensions that are given are for a compacted fill. (1) Assume you are in the design office, use both the Simpson Rule and Trapezoidal Rule to compute the total volume of earthworks required. (Assume both the dyke and the key will use the same material). (2) If you are a Contractor, how many days will it take to finish hauling the computed earthworks using 3 tippers of 12m³ each? Make appropriate assumptions. DIKE CROSS SECTION OGL KEY (FOUNDATION) 2m 1m 2m 8m Figure 1: Cross section of Dyke and its foundation 1.5m from highest OGL 0.5m…arrow_forwardThe parametric equations of the function are given as x = 3cos 0 - sin³0 and y = 3sin 0 - cos³0. dy d2y Calculate and dx dx².arrow_forward(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z ≤ 3}. Calculate the integral f(x, y, z) dv. Earrow_forward
- (12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.arrow_forward(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}. Calculate the integral y, f(x, y, z) dV.arrow_forward(14 points) Let f: R3 R and T: R3. →R³ be defined by f(x, y, z) = ln(x²+ y²+2²), T(p, 0,4)=(psin cos 0, psin sin, pcos). (a) (4 points) Write out the composition g(p, 0, 4) = (foT)(p,, ) explicitly. Then calculate the gradient Vg directly, i.e. without using the chain rule. (b) (4 points) Calculate the gradient Vf(x, y, z) where (x, y, z) = T(p, 0,4). (c) (6 points) Calculate the derivative matrix DT(p, 0, p). Then use the Chain Rule to calculate Vg(r,0,4).arrow_forward
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