Explanation Given: The derivative of the function is: f ' ( x ) = 2 x ( 4 x 2 − 10 ) 2 ; ( 2 , 10 ) Formula used: If f ' ( x ) is derivative of f ( x ) . Then, ∫ f ' ( x ) d x = f ( x ) The integration of x n is: ∫ x n d x = x n + 1 n + 1 + C The change of variable theorem for the indefinite integral: If u = g ( x ) . Then d u = g ' ( x ) d x . Then, the integral will take the following form: ∫ f ( g ( x ) ) g ' ( x ) d x = ∫ f ( u ) d u = F ( u ) + C Calculation: Consider the provided derivative of the function, f ' ( x ) = 2 x ( 4 x 2 − 10 ) 2 To find the equation of the function f ( x ) , integrate f ' ( x ) with respect to x . Then, f ( x ) = ∫ f ' ( x ) d x = ∫ 2 x ( 4 x 2 − 10 ) 2 d x Let, ( 4 x 2 − 10 ) = u

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Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 4.5, Problem 51E

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To calculate: The equation of the function whose derivative is given f'(x)=2x(4x2−10)2 ;(2,10).

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Chapter 4.5, Problem 48E

Chapter 4.5, Problem 52E

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 4 Solutions

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Ch. 4.1 - CONCEPT CHECK Antiderivative What does it mean for...Ch. 4.1 - Antiderivatives Can two different functions both...Ch. 4.1 - Particular Solution What is a particular solution...Ch. 4.1 - Prob. 4E Ch. 4.1 - Integration and Differentiation In Exercises 5 and...Ch. 4.1 - Integration and Differentiation In Exercises 5 and...Ch. 4.1 - Solving a Differential Equation In Exercises 7-10,...Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Solving a Differential Equation In Exercises 7-10,...

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The equation of the function whose derivative is given f ' ( x ) = 2 x ( 4 x 2 − 10 ) 2 ; ( 2 , 10 ) .

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To calculate: The equation of the function whose derivative is given f'(x)=2x(4x2−10)2 ;(2,10).

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Chapter 4 Solutions