EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 80, Problem 4A
To determine
Angle of rotation R and angle of tilt T.
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Q/ By using polar Coordinates show that the system
below has a limit cycle and show the stability of
+ his limit cycle:
X² = x + x(x² + y² -1)
y* = −x + y (x² + y²-1)
-x
xy
Q/Given H (X,Y) = ex-XX+1 be a first integral
find the corresponding system and study the
Stability of of critical point of this system.
Chapter 80 Solutions
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- Q/ show that H (X,Y) = x²-4x-x² is 2 first integral of the system Y° = y 0 y° = 2x + x 3 then study the stability of critical point and draw phase portrait.arrow_forwardQ/Given the function H (X,Y) = H (X,Y) = y 2 X2 2 2 ²** 3 as a first integral, find the correspoding for this function and draw the phase portrait-arrow_forwardQ/ show that the system has alimit cycle and draw phase portrait x = y + x ( 2-x²-y²)/(x² + y²) ½ 2 y = -x+y ( 2-x² - y²) / (x² + y²) ½/2arrow_forward
- A sequence X = (xn) is said to be a contractive sequence if there is a constant 0 < C < 1 so that for all n = N. - |Xn+1 − xn| ≤ C|Xn — Xn−1| -arrow_forwardPlease explain this theorem and proofarrow_forward3) Find the surface area of z -1≤ y ≤1 = 1 + x + y + x² over the rectangle -2 ≤ x ≤ 1 andarrow_forward
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