6. Solve and graph the function. Be sure to list any restrictions. [T/C-5 Marks/ x²-x-2 >...
2. (K/U: 6 marks and T: 6 marks) Solve for x. (a) 2x3 – 3x² – 8x +12<0 o bob UAH (b) log(x + 3) + log(x - 1) – log 21 = 0 (c) 32x+1 < 81
Solve the inequality f(x) <0, where f(x) = - x2(x + 4), by using the graph of the The solution set for f(x) <0 is. (Type your answer in interval notation.) function. Ay 4- 2- х 500 -8 -6 -4 -2 2 4. 6 -8- -104 -12-
Find f-1(x). f(x) = (x-1, x21 f-1(x) 2 n° +1 x State any restrictions on the domain of f-1(x). O x>-1 O x 20 x 2 1 x = 0 O x 1 x Use algebraic procedures to find the exact solution or solutions of the equation. (Enter your answers as a comma-separated list.) 5x + 1 = 291 x = 2.525 X
Q1 Given, f(x) = x + 1, 2 5 x < 4 4,0<x<2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval -12 < x < 12. (6 marks) (6) Determine the Fourier cosine coefficients of Q1(a). (10 marks) (c) Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks)
Sketch the graph of the resulting function. 2. Solve a" +x = 8(t - ) - 8(t-2r), z(0) = 0, z'(0) = 1. Sketch the graph of the result ing function. 3. Find a first order system corresponding to the scalar equation and find its general solution. (a) y"-44y= 0. (b) t2y"- 4ty+ 4y = 0, t > 0. (It general solution is of the form y(t) = ct+ cztt.) 4. Find the general solution to the system r'= Ar,...
Given, f(x) = {x #1, 2 5x<4 4,0<x< 2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval -12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Ql(a). (10 marks)
01 Given, f(x) = 4,05x<2 x + 1, 2 S x<4 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval – 12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Q1(a). (10 marks) (c) Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks) [Total: 20 marks)
Solve the inequality. Express your answer using interval notation Graph the solution set. (x+6)(x - 7)>(x - 4)(x+4) The solution to the inequality is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.)
Question 2: (26 marks) 2.1 Find the The Laplace transform of the following function t, if 03t<1 2t, if t1 [3] 2.2 Find the inverse Laplace transform of 10e 2 52 - 53 +632 - 25 + 5 (10] 2.3 Find y(4) if y(t) = u(t){t - 2)2 - us(t)/(t - 3) - 2) - us(t)e' (51 2.4 Solve the following initial value problem given by y" + 4y = 28.(t) (0)=1/(0) = 0 181 Question 3: (17 marks) Let...
Given, f(x) = {x +1,25x<4 4,0<x<2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval – 12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Ql(a). (10 marks) (c) Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks)