To determine To sketch: The graph of the given function and check by displaying the graph on a calculator. Explanation Features to be used in graphing functions: 1. Intercepts points for which the graph crosses each axis. 2. Tests for symmetry: a. A graph will have symmetry about the x -axis if it is same equation when all the y ’s are replaced with – y . b. A graph will have symmetry about the y -axis if it is same equation when all the x ’s are replaced with – x . c. A graph will have symmetry about the origin if it is same equation when all the y ’s are replaced with – y and all the x ’s are replaced with – x . 3. An asymptote is a line that the curve approaches as one of the variables approaches some particular value. 4. Vertical asymptotes: To find vertical asymptotes by finding values that make factors in the denominator zero. 5. Domain and range: The complete set of possible values of the independent variable is called the domain of the function and the complete set of all possible resulting values of the dependent variable is called the range of the function. 6. Derivatives we will find information from the first two derivatives. Calculation: The given function is y = e − x sin x . Obtain the x -intercept as follows. Substitute 0 for y in y = e − x sin x . 0 = e − x sin x sin x = 0 ( ∵ e − x ≠ 0 ) x = n π where n is integer Thus, the x -intercept is ( n π , 0 ) . Obtain the y -intercept as follows. Substitute 0 for x in y = e − x sin x . y = e 0 sin ( 0 ) = 0 Thus, the y -intercept is (0, 0). Check whether the given function is symmetry about x -axis, y -axis, and origin: All the y ’s are replaced with – y in the given function. − y = e − x sin x All the x ’s are replaced with – x in the given function. y = e − ( − x ) sin ( − x ) = − e x sin x All the y ’s are replaced with –y and all the x ’s are replaced with – x in the given function. − y = e − ( − x ) sin ( − x ) − y = − e x sin x y = e x sin x By the above result, there is no symmetry. Obtain the horizontal asymptote as follows. lim x → + ∞ y = lim x → + ∞ e − x sin x = lim x → + ∞ sin x e x = 0 Here, the range of the sine function is − 1 ≤ y ≤ 1 . Thus, the horizontal asymptote is y = 0. It is observed that the given function is no denominators. So, no vertical asymptotes. By the definition of domain, there is no undefined points. Thus, the domain of the function is set of all real numbers. Obtain the first derivative of y as follows. d y d x = d d x ( e − x sin x ) = e − x d d x ( sin x ) + ( sin x ) d d x ( e − x ) = e − x ( cos x ) + ( sin x ) ( − e − x ) = e − x ( cos x − sin x ) Obtain the second derivative of y as follows

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 27.8, Problem 12E

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Chapter 27.8, Problem 11E

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Chapter 27 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 27.1 - Prob. 1PE Ch. 27.1 - Prob. 2PE Ch. 27.1 - Prob. 1E Ch. 27.1 - Prob. 2E Ch. 27.1 - Prob. 3E Ch. 27.1 - Prob. 4E Ch. 27.1 - Prob. 5E Ch. 27.1 - Prob. 6E Ch. 27.1 - Prob. 7E Ch. 27.1 - Prob. 8E

Ch. 27.1 - Prob. 9E Ch. 27.1 - Prob. 10E Ch. 27.1 - Prob. 11E Ch. 27.1 - Prob. 12E Ch. 27.1 - Prob. 13E Ch. 27.1 - Prob. 14E Ch. 27.1 - Prob. 15E Ch. 27.1 - Prob. 16E Ch. 27.1 - Prob. 17E Ch. 27.1 - Prob. 18E Ch. 27.1 - Prob. 19E Ch. 27.1 - Prob. 20E Ch. 27.1 - Prob. 21E Ch. 27.1 - Prob. 22E Ch. 27.1 - Prob. 23E Ch. 27.1 - Prob. 24E Ch. 27.1 - Prob. 25E Ch. 27.1 - In Exercises 3–34, find the derivatives of the...Ch. 27.1 - Prob. 27E Ch. 27.1 - Prob. 28E Ch. 27.1 - Prob. 29E Ch. 27.1 - Prob. 30E Ch. 27.1 - Prob. 31E Ch. 27.1 - Prob. 32E Ch. 27.1 - Prob. 33E Ch. 27.1 - Prob. 34E Ch. 27.1 - Prob. 35E Ch. 27.1 - Prob. 36E Ch. 27.1 - Prob. 37E Ch. 27.1 - Prob. 38E Ch. 27.1 - Prob. 39E Ch. 27.1 - Prob. 40E Ch. 27.1 - Prob. 41E Ch. 27.1 - Prob. 42E Ch. 27.1 - Prob. 43E Ch. 27.1 - Prob. 44E Ch. 27.1 - Prob. 45E Ch. 27.1 - Prob. 46E Ch. 27.1 - Prob. 47E Ch. 27.1 - Prob. 48E Ch. 27.1 - Prob. 49E Ch. 27.1 - Prob. 50E Ch. 27.1 - Prob. 51E Ch. 27.1 - Prob. 52E Ch. 27.1 - Prob. 53E Ch. 27.1 - Prob. 54E Ch. 27.1 - 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In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 4E Ch. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 6E Ch. 27.8 - Prob. 7E Ch. 27.8 - Prob. 8E Ch. 27.8 - Prob. 9E Ch. 27.8 - Prob. 10E Ch. 27.8 - Prob. 11E Ch. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 13E Ch. 27.8 - Prob. 14E Ch. 27.8 - Prob. 15E Ch. 27.8 - Prob. 16E Ch. 27.8 - Prob. 17E Ch. 27.8 - Prob. 18E Ch. 27.8 - Prob. 19E Ch. 27.8 - Prob. 20E Ch. 27.8 - Prob. 21E Ch. 27.8 - Prob. 22E Ch. 27.8 - Prob. 23E Ch. 27.8 - Prob. 25E Ch. 27.8 - Prob. 26E Ch. 27.8 - Prob. 27E Ch. 27.8 - Prob. 28E Ch. 27.8 - Prob. 29E Ch. 27.8 - Prob. 30E Ch. 27.8 - Prob. 31E Ch. 27.8 - Prob. 32E Ch. 27.8 - Prob. 33E Ch. 27.8 - Prob. 34E Ch. 27.8 - The energy E (in J) dissipated by a certain...Ch. 27.8 - Prob. 36E Ch. 27.8 - Prob. 37E Ch. 27.8 - Prob. 39E Ch. 27.8 - A package of weather instruments is propelled into...Ch. 27.8 - Prob. 41E Ch. 27.8 - Prob. 42E Ch. 27.8 - Prob. 43E Ch. 27.8 - 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