Given f(x) = x2 - 6x +5, x<3 Graph f(x) and f-?(x) to show that they...
If 4 - x2 = f(x) < 4+x2 for –3 <x<3, find lim (2) 20
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]
Evaluate the piecewise defined function at the indicated values (x2 f(x) if x -1 6x if 1 < x s 1 = -1 if x > 1 f(-3) (- 3 2 f(-1) f(0) = f(30) =
Given the function: 6x - 1 2 < 0 63 - f(x) = 62 – 2 x > 0 Calculate the following values: f( - 1) = |-7 f(0) = f(2)
– 5x – 2 2 <1 Given the function t(x) 4.x2 - 6x +3 1< I< 5 - 3+1 I > 5 Calculate the following values: t(0) t(5) = t(2) = t(10) t(9) = t(1) =
Let f(x, y) = x2 – yż and D= {(2,y) : x2 + y2 < 4}. Let m and M be the absolute minimum and maximum values of f over D respectively. What is m - M?
sin (x - 1) x-TT x <T Given f(x) = x2 · Tex + 1, x > Determine if the graph is continuous at it (Show all work)
determine the fourier series if -2 Sto f(3) = { 1 + x2 if 0<<<2 f(x + 4) = f(x) - 5={17
Please show work on how to solve? (49. Show that the function (x2 +3 for x < 1 f(x) = 10 - x for 1 < x <2 6x - x2 for x > 2 is continuous for x + 1, 2. Then compute the right- and left-hand lim- its at x = 1, 2, and determine whether f is left-continuous, right- continuous, or continuous at these points (Figure 17). y = 10 - x > 9+ y=6x - x2...
x +1 if-2<x<3 |-x if x 23 8. Graph the function f(x)-