Explanation Given: The velocity v ( t ) is given by v ( t ) = 3 t + 1 . The time interval is given by [ 1 , 4 ] Number of sub-intervals is n = 4 Formula used: Formula to approximate the value of total distance traveled by an object moving with a velocity v ( t ) using Riemann sum for right end points and n sub-intervals is given by S n = ∑ k = 1 n | v ( a + k Δ t ) | ( Δ t ) Formula to approximate the value of total distance traveled by an object moving with a velocity v ( t ) using Riemann sum for right end points and n sub-intervals is given by S n = ∑ k = 1 n | v [ a + ( k − 1 ) Δ t ] | ( Δ t ) Where Δ t = b − a n Calculation: Consider the given velocity function. v ( t ) = 3 t + 1 Here, the interval is [ 1 , 4 ] . Therefore, b = 4 , a = 1 and n = 4 . Therefore, width of each sub-interval will be as shown. Δ t = b − a n = 4 − 1 4 = 3 4 = 0.75 Now, the points will be as follows: t 0 = a + 0 ( Δ t ) = 1 + 0 = 1 t 1 = 1 + Δ t = 1 + 0.75 = 1.75 t 2 = t 1 + Δ t = 1.75 + 0.75 = 2.50 t 3 = 3.25 t 4 = 4.0 Now, approximate the value of S n = ∑ k = 1 n | v ( a + k Δ t ) | ( Δ t ) for n = 4 . S 4 = ∑ k = 1 4 | v ( a + k Δ t ) | ( Δ t ) = ( Δ t ) | [ v ( t 1 ) + v ( t 2 ) + v ( t 3 ) + v ( t 4 ) ] | = ( 0

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 5.3, Problem 21PS

To determine

To calculate:The estimated value of total distance traveledby the object during given time interval using Riemann sum for 4 subintervals. Also compare the result for left end points and right end points as well.

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Chapter 5.3, Problem 20PS

Chapter 5.3, Problem 22PS

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Question 4 Find an equation of (a) The plane through the point (2, 0, 1) and perpendicular to the line x = y=2t, z=3+4t. 3t, (b) The plane through the point (3, −2, 8) and parallel to the plane z = x+y. (c) The plane that contains the line x = parallel to the plane 5x + 2y + z = 1. 1+t, y2t, z = 43t and is (d) The plane that passes through the point (1,2,3) and contains the line x = 3t, y=1+t, and z = 2 – t. (e) The plane that contains the lines L₁ : x = 1 + t, y = 1 − t, z = = L2 x 2s, y = s, z = 2. 2t and

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Chapter 5 Solutions

Student's Solution and Survival Manual for Calculus

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The estimated value of total distance traveledby the object during given time interval using Riemann sum for 4 subintervals. Also compare the result for left end points and right end points as well.

Solution Summary: The author calculates the estimated value of total distance traveled by the object during given time interval using Riemann sum for 4 subintervals.

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To calculate:The estimated value of total distance traveledby the object during given time interval using Riemann sum for 4 subintervals. Also compare the result for left end points and right end points as well.

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Chapter 5 Solutions