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
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 71E
Related questions
Question
(Question 56 and 89)
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F627ffe10-a730-4e4c-b7e9-b306478e5985%2F2c8c3f20-b0b4-45de-a620-2f3d83655874%2F3840jt_processed.jpeg&w=3840&q=75)
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
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F627ffe10-a730-4e4c-b7e9-b306478e5985%2F2c8c3f20-b0b4-45de-a620-2f3d83655874%2Fa1v4thn_processed.jpeg&w=3840&q=75)
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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