Sketch a geaph of x-4y=-8 Question 1 < Sketch a graph of I 4y = -...
Question 8 a) Sketch the graph of y=sin(x) and y=sin(2x) for 0<xs. b) Show that the area of the region bounded by these graphs is 4
Sketch a graph of the piecewise defined function. sz if x <3 f(x) = x 1 if x 2 3
1\x+21, x<0 -Sketch the graph of this piece-wise defined function: S(x) = {3 05x<2 1(x+1), x22
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)
x +1 if-2<x<3 |-x if x 23 8. Graph the function f(x)-
Need help with this question. Thank you :) Question 19. Sketch the graph of y = 3 sin (2x + 5), for -1 << < 1. Label the r and y intercepts. (Don't worry about labelling turning points or maxima or minima.)
U Question 22 1 pts Find the absolute minimum of f(x, y) = x2 + 4y? - 2x²y + 4 on the square given by -1 << < 1 and -1<y<1. 11 4 8 None of the above or below O-2 07
Q1 Given, f(x) = {x 4,0<x< 2 1x + 1, 2<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) () Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks)
Consider the following. 1, -LSX<0. 10. OSX<L; f(x + 2) = f(x) (a) Sketch the graph of the given function for three periods. (In these graphs, L = 1.) f(x) — — - - - 1 -3 -2 -1 1 2 -3 3 3 -2 -1 . 2 1 (b) Find the Fourier series for the given function. R0 - 4 - ŠOx)
Q1 Given, f(x) = {, 4,05x<2 6x + 1, 2 <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]