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56. The region bounded by the graph of f(x) = 3x² + 1 and the x-axis on the interval [-1, 1].

56. The region bounded by the graph of f(x) = 3x² + 1 and the x-axis on the interval [-1, 1].

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 71E
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T 55-58. Approximating areas with a calculator Use a calculator and right Riemann sums to approximate the area of the given region. Present your calculations in a table showing the approximations for n = 10, 30, 60, and 80 subintervals. Make a conjecture about the limit of Riemann sums as n → ∞0. 55. The region bounded by the graph of f(x) = 12 - 3x² and the x-axis on the interval [−1, 1]. 56. The region bounded by the graph of f(x) = 3x² + 1 and the x-axis on the interval [-1, 1]. 57. The region bounded by the graph of f(x) the interval [-T, π]. 58. The region bounded by the graph of f(x) = (2ª + 2¯³) In 2 and the x- axis on the interval [-2, 2]. = 1 - cos x 2 and the x-axis on
Transcribed Image Text:T 55-58. Approximating areas with a calculator Use a calculator and right Riemann sums to approximate the area of the given region. Present your calculations in a table showing the approximations for n = 10, 30, 60, and 80 subintervals. Make a conjecture about the limit of Riemann sums as n → ∞0. 55. The region bounded by the graph of f(x) = 12 - 3x² and the x-axis on the interval [−1, 1]. 56. The region bounded by the graph of f(x) = 3x² + 1 and the x-axis on the interval [-1, 1]. 57. The region bounded by the graph of f(x) the interval [-T, π]. 58. The region bounded by the graph of f(x) = (2ª + 2¯³) In 2 and the x- axis on the interval [-2, 2]. = 1 - cos x 2 and the x-axis on
T 87-90. Graphing general solutions Graph several functions that satisfy each of the following differential equations. Then find and graph the particular function that satisfies the given initial condition. 87. f'(x) = 2x – 5; ƒ(0) = 4 = 88. f'(x) = 3x² - 1; f(1) = 2 89. f'(x) 3x sin x; f(0) = 3 90. f'(x) = cos x - sin x + 2; f(0) = 1 =
Transcribed Image Text:T 87-90. Graphing general solutions Graph several functions that satisfy each of the following differential equations. Then find and graph the particular function that satisfies the given initial condition. 87. f'(x) = 2x – 5; ƒ(0) = 4 = 88. f'(x) = 3x² - 1; f(1) = 2 89. f'(x) 3x sin x; f(0) = 3 90. f'(x) = cos x - sin x + 2; f(0) = 1 =
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