2. In this exercise you are asked to prove (i.e., present convincing arguments) the symmetry prin- ciple, that was stated in class. Let R be the region under the graph of y = f(x) over [-a, a], where f(x) > 0. Assume that R is symmetric with respect to y-axis. (a) Give the definitions for even and odd functions. What are geometric properties of the graphs of even and odd functions? Provide some geometric examples. (b) Explain why y = f(x) in the problem is even. You may want to start with the definition of a symmetric object. (c) Show that y = xf(x) is odd. (d) Using the previous point show that M, = 0. (e) Show that the center of mass of R lays on the y-axis.

2. In this exercise you are asked to prove (i.e., present convincing arguments) the symmetry prin- ciple, that was stated in class. Let R be the region under the graph of y = f(x) over [-a, a], where f(x) > 0. Assume that R is symmetric with respect to y-axis. (a) Give the definitions for even and odd functions. What are geometric properties of the graphs of even and odd functions? Provide some geometric examples. (b) Explain why y = f(x) in the problem is even. You may want to start with the definition of a symmetric object. (c) Show that y = xf(x) is odd. (d) Using the previous point show that M, = 0. (e) Show that the center of mass of R lays on the y-axis.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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