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For this system of two equations y = cos² (x), x² + y² = x² = 2₁ - a. Plot the two equations and observe two intersections that occur near x 2 and x = -1. =

For this system of two equations y = cos² (x), x² + y² = x² = 2₁ - a. Plot the two equations and observe two intersections that occur near x 2 and x = -1. =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For this system of two equations y = cos² (x), x² + y² − x = 2, a. Plot the two equations and observe two intersections -1. that occur near x = 2 and x = b. Substitute y from the first equation into the second, getting an equation in only x. Solve this equation for the x-value (s) by any of the methods in this chapter to find where the function is zero, then substitute this x-value in either of the original equations to get y-values. c. Repeat part (b) but now solve for x from one equa- tion and use it to eliminate x from the other. You should get the same solutions, of course, but which is easier to use?
Transcribed Image Text:For this system of two equations y = cos² (x), x² + y² − x = 2, a. Plot the two equations and observe two intersections -1. that occur near x = 2 and x = b. Substitute y from the first equation into the second, getting an equation in only x. Solve this equation for the x-value (s) by any of the methods in this chapter to find where the function is zero, then substitute this x-value in either of the original equations to get y-values. c. Repeat part (b) but now solve for x from one equa- tion and use it to eliminate x from the other. You should get the same solutions, of course, but which is easier to use?
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