Explanation Given: The indefinite integral, ∫ ( a sin ( b x ) − c ) d x . Concept Used: ∫ sin x d x = − cos x Sum rule of indefinite integrals: ∫ ( f ( x ) + g ( x ) ) d x = ∫ f ( x ) d x + ∫ g ( x ) d x Constant multiple rule of indefinite integrals: ∫ k f ( x ) d x = k ∫ f ( x ) d x , where k is a constant. Calculation: In order to find the value of the indefinite integral ∫ ( a sin ( b x ) − c ) d x , use the sum of indefinite integrals rule and simplify further using the u -substitution method

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 4.4, Problem 68S

To determine

To solve the indefinite integral ∫(asin( bx)−c) dx , where a , b , and c are real numbers with a≠0, b≠0, c>0, and c≠1 .

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Chapter 4.4, Problem 67S

Chapter 4.4, Problem 69A

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Evaluate the limit along the stated paths, or type "DNE" if the limit Does Not Exist: lim xy+y³ (x,y)(0,0) x²+ y² Along the path = = 0: Along the path y = = 0: Along the path y = 2x:

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A graph of the function f is given below: Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1 Of is defined at a. If is not defined at x = a. Of is continuous at x = a. If is discontinuous at x = a. Of is smooth at x = a. Of is not smooth at = a. If has a horizontal tangent line at = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. If has no tangent line at x = a. f(a + h) - f(a) lim is finite. h→0 h f(a + h) - f(a) lim h->0+ and lim h h->0- f(a + h) - f(a) h are infinite. lim does not exist. h→0 f(a+h) - f(a) h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

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To solve the indefinite integral ∫ ( a sin ( b x ) − c ) d x , where a , b , and c are real numbers with a ≠ 0 , b ≠ 0 , c > 0 , and c ≠ 1 .

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To solve the indefinite integral ∫ ( a sin ( b x ) − c ) d x , where a , b , and c are real numbers with a ≠ 0 , b ≠ 0 , c > 0 , and c ≠ 1 .