2. Show that the following systems have no periodic orbits provided the pa- iy+ar2 +by2 [2 marks]...
1. Show that the following systems have no periodic orbits. 1 marlk 3 marks 1. Show that the following systems have no periodic orbits. 1 marlk 3 marks
For each of the following systems, find a > 0 and b > 0 such that L(x, y) = ax^2 + by^2 obeys d/dt(L) not = 0 whenever (x, y) 6= (0, 0). (This makes L a Liapounov function.) State whether the origin is a stable or unstable equilibrium in each case. (a) x' = −x^3 + 7xy^2 , y' = −3x^2y + y^3 . (b) x' = x^3 − y^3 , y' = 3xy^2 + 4x^2 y + 5y^3...
Problem 2: (2 marks) By considering different paths of approach, show that the following functions have no limit. lim - 9x’y (x,y (0,0) ** - 13y3
Fourier Series. Thank you in advance. Q 2(a) [6 Marks] (i) Sketch 3 successive cycles of the periodic function g(t):[4 marks) g() gt3). (ii) Is g(t)an even or odd function of? [2 marks] [14 Marks] (i) Show that the Fourier series coefficients of gl), as defined in part 2(a), may Q 2(b) [11 marks]: be written as follows 0, EVEN (ii) Obtain a value for the constant [3 marks] [5 Marks Q 2(c) What is the power, or mean-squared value,...
Problem 2 125 Marks Given the following periodic signal: 5-3-2 e) a- Find the trigonometric Fourier series, sketch the amplitude, and phase spectra. [15 Marks] Student b- Does the signal has a de component? Exp Explain. [5 Marks] If you are given the signal x(t) = tu (t). Can we write the Fourier series of the signal in the period 0 t < 1? Explain. [5 Marks] c-
2.[12 marks] The following problems cellation error. are about roundoff error - Can- Determine a way how to compute the following functions more accu- rately, i.e., how one can avoid cancellation error effectively. (1). 14 marks] fi(x) = x - Vx - 3 when x is large (2). [4 marks] f2(x) = 2 (1 - cos x) when r is near 0. (3). /4 marks] When one applies the quadratic formula 4ac -b+ Vb -4ac -b- 2a 2a 0, where...
microcomputer systems 2) 19 marks) For each of the following code fragments, determine which of the branches are taken, not taken, or cannot be determined. Note the Bxx is used to represent a generic branch instruction. Show your work. A) LDAA #$42 CMPA #$C1 Bxcx target B) LDAA #$41 ADDA #$2C CMPA #$9A Bxx target C) LDAA #$21 COMA CMPA #$F1 Bxx target D) LDAA #$27 NEGA CMPA #$27 Bxx target T= taken, NT = Not taken, CBD = Cannot...
no excel work, show formula please You have done your research for the following investments and your friend has provided their expectations for the markets for next year. Probability of State of State of Stock Stock Economy Economy A B TSX Boom .30 30% -9% 18% Normal .40 16% 12% 10% Recession .30 -10% 20% -10% Remember to show all of your work * h. Calculate the covariance and correlation of the returns for stock A and the TSX. (2...
Show the partial fraction decomposition for the following expressions a) x-100 (2 marks) 2+8x-48 x+-34x +21x +145 -4x2 -3x+18 (2 marks) b) (2 marks) i) For each partial fraction decomposition answer from part a) use the expression i) Comment on the significance of the results. Show the partial fraction decomposition for the following expressions a) x-100 (2 marks) 2+8x-48 x+-34x +21x +145 -4x2 -3x+18 (2 marks) b) (2 marks) i) For each partial fraction decomposition answer from part a) use...
You have done your research for the following investments and your friend has provided their expectations for the markets for next year. Probability of State of State of Stock Stock Economy Economy A B TSX Boom .30 30% -9% 18% Normal .40 16% 12% 10% Recession .30 -10% 20% -10% * Remember to show all of your work * a. Calculate the expected return for stock A. (2 marks) b. Calculate the expected return for stock B. (2 marks) C....