Let f(x) = 14 - 2x. (a) Sketch the region R under the graph of f on the interval [0, 7]. y 15 10 y 15 10 10 Find its exact area (in square units) using geometry. square units (b) Use a Riemann sum with five subintervals of equal length (n = 5) to approximate the area (in square units) of R. Choose the representative points to be the right endpoints of the subintervals. square units (c) Repeat part (b) with ten subintervals of equal length (n = 10). square units (d) Compare the approximations obtained in parts (b) and (c) with the exact area found in part (a). Do the approximations improve with larger n? Yes No

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 32RE
Question
Let f(x)
= 14 - 2x.
(a) Sketch the region R under the graph of f on the interval [0, 7].
y
15
10
y
15
10
10
Transcribed Image Text:Let f(x) = 14 - 2x. (a) Sketch the region R under the graph of f on the interval [0, 7]. y 15 10 y 15 10 10
Find its exact area (in square units) using geometry.
square units
(b) Use a Riemann sum with five subintervals of equal length (n = 5) to approximate the area (in square units) of R. Choose the representative points to be the right endpoints of the
subintervals.
square units
(c) Repeat part (b) with ten subintervals of equal length (n = 10).
square units
(d) Compare the approximations obtained in parts (b) and (c) with the exact area found in part (a). Do the approximations improve with larger n?
Yes
No
Transcribed Image Text:Find its exact area (in square units) using geometry. square units (b) Use a Riemann sum with five subintervals of equal length (n = 5) to approximate the area (in square units) of R. Choose the representative points to be the right endpoints of the subintervals. square units (c) Repeat part (b) with ten subintervals of equal length (n = 10). square units (d) Compare the approximations obtained in parts (b) and (c) with the exact area found in part (a). Do the approximations improve with larger n? Yes No
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