Explanation Formula used: Slope of a line: For a function y = f ( x ) , the point P ( x 1 , y 1 ) can be written as, P ( x 1 , f ( x 1 ) ) and any other point Q ( x 2 , y 2 ) can be written as, Q ( x 1 + h , f ( x 1 + h ) ) , where h is defined as, h = x 2 − x 1 . Then, the slope of the line PQ is expressed as, m P Q = f ( x 1 + h ) − f ( x 1 ) ( x 1 + h ) − ( x 1 ) = f ( x 1 + h ) − f ( x 1 ) h Calculation: The given curve is y = 1 3 x 3 + x with the x values 1 and 2. Obtain the slope of the lines which is tangent to the curve as follows. The curve is y = 1 3 x 3 + x . That is, f ( x ) = 1 3 x 3 + x . With respect to the above mentioned formula, the slope of PQ is computed as follows. m P Q = f ( x 1 + h ) − f ( x 1 ) h = [ 1 3 ( x 1 + h ) 3 + ( x 1 + h ) ] − [ 1 3 ( x 1 ) 3 + ( x 1 ) ] h </

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Chapter 23.2, Problem 32E

To determine

The slope of the tangent lines to the curve y=13x3+x where the x values are 1 and 2. Also find the acute angle at the point of intersection of these lines.

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Chapter 23.2, Problem 31E

Chapter 23.2, Problem 33E

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Chapter 23 Solutions

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Ch. 23.1 - Determine the continuity of the function . Ch. 23.1 - Prob. 2PE Ch. 23.1 - Find . Ch. 23.1 - Find . Ch. 23.1 - Prob. 1E Ch. 23.1 - Prob. 2E Ch. 23.1 - Prob. 3E Ch. 23.1 - Prob. 4E Ch. 23.1 - Prob. 5E Ch. 23.1 - Prob. 6E

Ch. 23.1 - Prob. 7E Ch. 23.1 - Prob. 8E Ch. 23.1 - Prob. 9E Ch. 23.1 - Prob. 10E Ch. 23.1 - Prob. 11E Ch. 23.1 - Prob. 12E Ch. 23.1 - Prob. 13E Ch. 23.1 - Prob. 14E Ch. 23.1 - Prob. 15E Ch. 23.1 - Prob. 16E Ch. 23.1 - Prob. 17E Ch. 23.1 - Prob. 18E Ch. 23.1 - Prob. 19E Ch. 23.1 - Prob. 20E Ch. 23.1 - In Exercises 21–24, graph the function and...Ch. 23.1 - Prob. 22E Ch. 23.1 - Prob. 23E Ch. 23.1 - Prob. 24E Ch. 23.1 - Prob. 25E Ch. 23.1 - Prob. 26E Ch. 23.1 - Prob. 27E Ch. 23.1 - Prob. 28E Ch. 23.1 - Prob. 29E Ch. 23.1 - Prob. 30E Ch. 23.1 - Prob. 31E Ch. 23.1 - Prob. 32E Ch. 23.1 - Prob. 33E Ch. 23.1 - Prob. 34E Ch. 23.1 - Prob. 35E Ch. 23.1 - Prob. 36E Ch. 23.1 - Prob. 37E Ch. 23.1 - Prob. 38E Ch. 23.1 - Prob. 39E Ch. 23.1 - Prob. 40E Ch. 23.1 - Prob. 41E Ch. 23.1 - Prob. 42E Ch. 23.1 - Prob. 43E Ch. 23.1 - Prob. 44E Ch. 23.1 - Prob. 45E Ch. 23.1 - In Exercises 31–50, evaluate the indicated limits...Ch. 23.1 - In Exercises 31–50, evaluate the indicated limits...Ch. 23.1 - Prob. 48E Ch. 23.1 - Prob. 49E Ch. 23.1 - Prob. 50E Ch. 23.1 - Prob. 51E Ch. 23.1 - Prob. 52E Ch. 23.1 - Prob. 53E Ch. 23.1 - Prob. 54E Ch. 23.1 - Prob. 55E Ch. 23.1 - Prob. 56E Ch. 23.1 - Prob. 57E Ch. 23.1 - Prob. 58E Ch. 23.1 - Prob. 59E Ch. 23.1 - A 5-Ω resistor and a variable resistor of...Ch. 23.1 - Prob. 61E Ch. 23.1 - Prob. 62E Ch. 23.1 - Prob. 63E Ch. 23.1 - Prob. 64E Ch. 23.1 - Prob. 65E Ch. 23.1 - Prob. 66E Ch. 23.1 - Prob. 67E Ch. 23.1 - Prob. 68E Ch. 23.1 - Prob. 69E Ch. 23.1 - Prob. 70E Ch. 23.1 - Prob. 71E Ch. 23.1 - Prob. 72E Ch. 23.2 - Find the slope of a line tangent to the curve of y...Ch. 23.2 - Prob. 2PE Ch. 23.2 - Prob. 1E Ch. 23.2 - Prob. 2E Ch. 23.2 - In Exercises 3–6, use the method of Example 1 to...Ch. 23.2 - In Exercises 3–6, use the method of Example 1 to...Ch. 23.2 - Prob. 5E Ch. 23.2 - Prob. 6E Ch. 23.2 - In Exercises 7–10, use the method of Example 2 to...Ch. 23.2 - Prob. 8E Ch. 23.2 - Prob. 9E Ch. 23.2 - Prob. 10E Ch. 23.2 - Prob. 11E Ch. 23.2 - Prob. 12E Ch. 23.2 - Prob. 13E Ch. 23.2 - Prob. 14E Ch. 23.2 - Prob. 15E Ch. 23.2 - Prob. 16E Ch. 23.2 - Prob. 17E Ch. 23.2 - Prob. 18E Ch. 23.2 - Prob. 19E Ch. 23.2 - Prob. 20E Ch. 23.2 - Prob. 21E Ch. 23.2 - Prob. 22E Ch. 23.2 - Prob. 23E Ch. 23.2 - Prob. 24E Ch. 23.2 - Prob. 25E Ch. 23.2 - Prob. 26E Ch. 23.2 - In Exercises 27–30, find the point(s) where the...Ch. 23.2 - Prob. 28E Ch. 23.2 - Prob. 29E Ch. 23.2 - Prob. 30E Ch. 23.2 - Prob. 31E Ch. 23.2 - Prob. 32E Ch. 23.2 - Prob. 33E Ch. 23.2 - Prob. 34E Ch. 23.3 - Using the definiton, find the derivative of y = 5x...Ch. 23.3 - Prob. 2PE Ch. 23.3 - Prob. 1E Ch. 23.3 - Prob. 2E Ch. 23.3 - Prob. 3E Ch. 23.3 - Prob. 4E Ch. 23.3 - Prob. 5E Ch. 23.3 - Prob. 6E Ch. 23.3 - Prob. 7E Ch. 23.3 - Prob. 8E Ch. 23.3 - Prob. 9E Ch. 23.3 - Prob. 10E Ch. 23.3 - Prob. 11E Ch. 23.3 - Prob. 12E Ch. 23.3 - Prob. 13E Ch. 23.3 - Prob. 14E Ch. 23.3 - Prob. 15E Ch. 23.3 - Prob. 16E Ch. 23.3 - Prob. 17E Ch. 23.3 - Prob. 18E Ch. 23.3 - Prob. 19E Ch. 23.3 - Prob. 20E Ch. 23.3 - Prob. 21E Ch. 23.3 - Prob. 22E Ch. 23.3 - Prob. 23E Ch. 23.3 - Prob. 24E Ch. 23.3 - In Exercises 25–28, find the derivative of each...Ch. 23.3 - Prob. 26E Ch. 23.3 - Prob. 27E Ch. 23.3 - Prob. 28E Ch. 23.3 - Prob. 29E Ch. 23.3 - Prob. 30E Ch. 23.3 - Prob. 31E Ch. 23.3 - Prob. 32E Ch. 23.3 - Prob. 33E Ch. 23.3 - Prob. 34E Ch. 23.3 - Prob. 35E Ch. 23.3 - Prob. 36E Ch. 23.3 - Prob. 37E Ch. 23.3 - Prob. 38E Ch. 23.3 - Prob. 39E Ch. 23.3 - Prob. 40E Ch. 23.4 - Prob. 1PE Ch. 23.4 - Prob. 2PE Ch. 23.4 - Prob. 1E Ch. 23.4 - Prob. 2E Ch. 23.4 - Prob. 3E Ch. 23.4 - Prob. 4E Ch. 23.4 - Prob. 5E Ch. 23.4 - Prob. 6E Ch. 23.4 - Prob. 7E Ch. 23.4 - Prob. 8E Ch. 23.4 - Prob. 9E Ch. 23.4 - Prob. 10E Ch. 23.4 - Prob. 11E Ch. 23.4 - Prob. 12E Ch. 23.4 - Prob. 13E Ch. 23.4 - Prob. 14E Ch. 23.4 - Prob. 15E Ch. 23.4 - Prob. 16E Ch. 23.4 - Prob. 17E Ch. 23.4 - Prob. 18E Ch. 23.4 - Prob. 19E Ch. 23.4 - Prob. 20E Ch. 23.4 - Prob. 21E Ch. 23.4 - Prob. 22E Ch. 23.4 - Prob. 23E Ch. 23.4 - Prob. 24E Ch. 23.4 - Prob. 25E Ch. 23.4 - Prob. 26E Ch. 23.4 - Prob. 27E Ch. 23.4 - Prob. 28E Ch. 23.4 - Prob. 29E Ch. 23.4 - Prob. 30E Ch. 23.4 - Prob. 31E Ch. 23.4 - Prob. 32E Ch. 23.4 - Prob. 33E Ch. 23.4 - Prob. 34E Ch. 23.4 - Prob. 35E Ch. 23.4 - Prob. 36E Ch. 23.4 - Prob. 37E Ch. 23.4 - Prob. 38E Ch. 23.4 - Prob. 39E Ch. 23.4 - Prob. 40E Ch. 23.4 - Prob. 41E Ch. 23.4 - Prob. 42E Ch. 23.4 - In Exercises 27–46, find the indicated...Ch. 23.4 - Prob. 44E Ch. 23.4 - Prob. 45E Ch. 23.4 - Prob. 46E Ch. 23.5 - Prob. 1PE Ch. 23.5 - Prob. 2PE Ch. 23.5 - Prob. 1E Ch. 23.5 - Prob. 2E Ch. 23.5 - Prob. 3E Ch. 23.5 - Prob. 4E Ch. 23.5 - Prob. 5E Ch. 23.5 - Prob. 6E Ch. 23.5 - Prob. 7E Ch. 23.5 - Prob. 8E Ch. 23.5 - Prob. 9E Ch. 23.5 - Prob. 10E Ch. 23.5 - Prob. 11E Ch. 23.5 - In Exercises 5–20, find the derivative of each of...Ch. 23.5 - Prob. 13E Ch. 23.5 - Prob. 14E Ch. 23.5 - Prob. 15E Ch. 23.5 - Prob. 16E Ch. 23.5 - Prob. 17E Ch. 23.5 - Prob. 18E Ch. 23.5 - Prob. 19E Ch. 23.5 - Prob. 20E Ch. 23.5 - Prob. 21E Ch. 23.5 - Prob. 22E Ch. 23.5 - Prob. 23E Ch. 23.5 - Prob. 24E Ch. 23.5 - 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Do not multiply factors...Ch. 23.6 - Prob. 2PE Ch. 23.6 - Prob. 1E Ch. 23.6 - Prob. 2E Ch. 23.6 - Prob. 3E Ch. 23.6 - Prob. 4E Ch. 23.6 - Prob. 5E Ch. 23.6 - Prob. 6E Ch. 23.6 - Prob. 7E Ch. 23.6 - Prob. 8E Ch. 23.6 - Prob. 9E Ch. 23.6 - Prob. 10E Ch. 23.6 - Prob. 11E Ch. 23.6 - Prob. 12E Ch. 23.6 - Prob. 13E Ch. 23.6 - Prob. 14E Ch. 23.6 - Prob. 15E Ch. 23.6 - Prob. 16E Ch. 23.6 - Prob. 17E Ch. 23.6 - Prob. 18E Ch. 23.6 - Prob. 19E Ch. 23.6 - Prob. 20E Ch. 23.6 - Prob. 21E Ch. 23.6 - Prob. 22E Ch. 23.6 - Prob. 23E Ch. 23.6 - Prob. 24E Ch. 23.6 - Prob. 25E Ch. 23.6 - Prob. 26E Ch. 23.6 - Prob. 27E Ch. 23.6 - Prob. 28E Ch. 23.6 - Prob. 29E Ch. 23.6 - Prob. 30E Ch. 23.6 - Prob. 31E Ch. 23.6 - Prob. 32E Ch. 23.6 - Prob. 33E Ch. 23.6 - Prob. 34E Ch. 23.6 - Prob. 35E Ch. 23.6 - Prob. 36E Ch. 23.6 - Prob. 37E Ch. 23.6 - Prob. 38E Ch. 23.6 - Prob. 39E Ch. 23.6 - Prob. 40E Ch. 23.6 - Prob. 41E Ch. 23.6 - Prob. 42E Ch. 23.6 - Prob. 43E Ch. 23.6 - Prob. 44E Ch. 23.6 - In Exercises 33–58, solve the given problems by...Ch. 23.6 - 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Prob. 29E Ch. 23.7 - Prob. 30E Ch. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 32E Ch. 23.7 - Prob. 33E Ch. 23.7 - Prob. 34E Ch. 23.7 - Prob. 35E Ch. 23.7 - Prob. 36E Ch. 23.7 - Prob. 37E Ch. 23.7 - Prob. 38E Ch. 23.7 - Prob. 39E Ch. 23.7 - Prob. 40E Ch. 23.7 - Prob. 41E Ch. 23.7 - Prob. 42E Ch. 23.7 - Prob. 43E Ch. 23.7 - Prob. 44E Ch. 23.7 - Prob. 45E Ch. 23.7 - Prob. 46E Ch. 23.7 - Prob. 47E Ch. 23.7 - Prob. 48E Ch. 23.7 - Prob. 49E Ch. 23.7 - Prob. 50E Ch. 23.7 - Prob. 51E Ch. 23.7 - Prob. 52E Ch. 23.7 - Prob. 53E Ch. 23.7 - Prob. 54E Ch. 23.7 - Prob. 55E Ch. 23.7 - Prob. 56E Ch. 23.7 - Prob. 57E Ch. 23.7 - Prob. 58E Ch. 23.8 - Prob. 1PE Ch. 23.8 - Prob. 1E Ch. 23.8 - Prob. 2E Ch. 23.8 - In Exercises 3–22, find dy/dx by differentiating...Ch. 23.8 - Prob. 4E Ch. 23.8 - Prob. 5E Ch. 23.8 - Prob. 6E Ch. 23.8 - Prob. 7E Ch. 23.8 - Prob. 8E Ch. 23.8 - Prob. 9E Ch. 23.8 - Prob. 10E Ch. 23.8 - Prob. 11E Ch. 23.8 - Prob. 12E Ch. 23.8 - Prob. 13E Ch. 23.8 - Prob. 14E Ch. 23.8 - 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Prob. 15RE Ch. 23 - Prob. 16RE Ch. 23 - Prob. 17RE Ch. 23 - Prob. 18RE Ch. 23 - Prob. 19RE Ch. 23 - Prob. 20RE Ch. 23 - In Exercises 21–28, use the definition to find the...Ch. 23 - Prob. 22RE Ch. 23 - Prob. 23RE Ch. 23 - Prob. 24RE Ch. 23 - Prob. 25RE Ch. 23 - Prob. 26RE Ch. 23 - Prob. 27RE Ch. 23 - Prob. 28RE Ch. 23 - Prob. 29RE Ch. 23 - Prob. 30RE Ch. 23 - Prob. 31RE Ch. 23 - Prob. 32RE Ch. 23 - Prob. 33RE Ch. 23 - Prob. 34RE Ch. 23 - Prob. 35RE Ch. 23 - Prob. 36RE Ch. 23 - Prob. 37RE Ch. 23 - Prob. 38RE Ch. 23 - Prob. 39RE Ch. 23 - Prob. 40RE Ch. 23 - Prob. 41RE Ch. 23 - Prob. 42RE Ch. 23 - Prob. 43RE Ch. 23 - Prob. 44RE Ch. 23 - Prob. 45RE Ch. 23 - Prob. 46RE Ch. 23 - Prob. 47RE Ch. 23 - Prob. 48RE Ch. 23 - Prob. 49RE Ch. 23 - Prob. 50RE Ch. 23 - Prob. 51RE Ch. 23 - Prob. 52RE Ch. 23 - Prob. 53RE Ch. 23 - Prob. 54RE Ch. 23 - Prob. 55RE Ch. 23 - Prob. 56RE Ch. 23 - Prob. 57RE Ch. 23 - Prob. 58RE Ch. 23 - Prob. 59RE Ch. 23 - Prob. 60RE Ch. 23 - Prob. 61RE Ch. 23 - Prob. 62RE Ch. 23 - Prob. 63RE Ch. 23 - Prob. 64RE Ch. 23 - If $5000 is invested at interest rate i,...Ch. 23 - The temperature T (in °C) of a rotating machine...Ch. 23 - Prob. 67RE Ch. 23 - Prob. 68RE Ch. 23 - Prob. 69RE Ch. 23 - Prob. 70RE Ch. 23 - Prob. 71RE Ch. 23 - Prob. 72RE Ch. 23 - Prob. 73RE Ch. 23 - Prob. 74RE Ch. 23 - Prob. 75RE Ch. 23 - Prob. 76RE Ch. 23 - Prob. 77RE Ch. 23 - Prob. 78RE Ch. 23 - Prob. 79RE Ch. 23 - Prob. 80RE Ch. 23 - Prob. 81RE Ch. 23 - Prob. 82RE Ch. 23 - Prob. 83RE Ch. 23 - Prob. 84RE Ch. 23 - Prob. 85RE Ch. 23 - Prob. 86RE Ch. 23 - Prob. 87RE Ch. 23 - Prob. 88RE Ch. 23 - Prob. 89RE Ch. 23 - Prob. 90RE Ch. 23 - Prob. 91RE Ch. 23 - Prob. 92RE Ch. 23 - Prob. 93RE Ch. 23 - Prob. 94RE Ch. 23 - Prob. 95RE Ch. 23 - Prob. 96RE Ch. 23 - Prob. 97RE Ch. 23 - Prob. 98RE Ch. 23 - In Exercises 53–98, solve the given problems. 99....Ch. 23 - Prob. 1PT Ch. 23 - Prob. 2PT Ch. 23 - Prob. 3PT Ch. 23 - Prob. 4PT Ch. 23 - Prob. 5PT Ch. 23 - Prob. 6PT Ch. 23 - Prob. 7PT Ch. 23 - Prob. 8PT Ch. 23 - 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The slope of the tangent lines to the curve y = 1 3 x 3 + x where the x values are 1 and 2. Also find the acute angle at the point of intersection of these lines.

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The slope of the tangent lines to the curve y=13x3+x where the x values are 1 and 2. Also find the acute angle at the point of intersection of these lines.

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Chapter 23 Solutions