< x < a be 27 periodic functions. Project 13. (6 points) Let g(x) = x4...
5) In Coul, with inner product < f g >= $(x)g(x)dx, let f(x) = x”,g(x) = x, a) Compute< x,x?>; b) Find the "angle" between the two functions.
Let f(x) = 3x – 6 and g(x) = 6x + 5. Write a formula for each of the following functions and then simplify e. fg= Preview f. ff= Preview
1. If fand g are both even functions, is the product fg even? If f and g both odd functions, is fg odd? What if f is even and g is odd? Justify your answers. (10 points) Find the domain g(x) =-. (10 points) 2. of the composited function fog, where f(x)=x+ and x +1 x+2 3. Let ifx <1 g(x) = x-3 ifx >2 Evaluate each of the following, if it exists. (10 points) lim g(x) lim gx)(i) lim...
5) In C.), with inner product <f,g> [f(x)g(x)dx, let f(x) = x², g(x)= x', a) Compute< x², x? >; 0 b) Find the “angle” between the two functions.
1. (25 points) Let f (x, y) = x4 - 4xy + y2 (6 points) Find fr.fy a. b. (9 points) Find fxx fry, fry c. (6 points) Find all critical points.
1. (25 points) Let f (x, y) = x4 - 4xy + y2 (6 points) Find fr.fy a. b. (9 points) Find fxx fry, fry c. (6 points) Find all critical points.
Problem #6: Let 58 0 < t <a f(0) = -8 x<I< 27 and assume that when f(t) is extended to the negative t-axis in a periodic manner, the resulting function is even Consider the following differential equation. 3 d2x de 2 + 7x = $(1) Find a particular solution of the above differential equation of the form 00 00 Xp(1) git,n) P and enter the function g(t, ) into the answer box below.
11. (10 points) Let f(t) be a 27-periodic function defined by f(t) = -{ 2 if – <t<0, -2 if 0 <t<, f(t + 2) = f(t). a) Find the Fourier series of f(t). b) What is the sum of the Fourier series of f at t = /2.
2a) Let a, b e R with a < b and let g [a, bR be continuous. Show that g(x) cos(nx) dx→ 0 n →oo. as Hint: Let ε > 0, By uniform continuity of g, there exists δ > 0 such that 2(b - a Choose points a = xo < x1 < . . . < Xm such that Irh-1-2k| < δ. Then we may write rb g (z) cos(nx) dx = An + Bn where 7m (g(x)...
6. (6 points) Let f(x) = 3x and let g(x) be the function shown in Figure 1. Determine So f()g'(x)dx. Figure 1: Graph of g() 1.5 + 1 9(0) -0. 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 -0.5 +
6: Problem 1 Previous Problem Problem List Next Problem (2 points) Let f(x) = z* In(t)dt (a) Evaluate f'(10) = (b) Evaluate (8-1)'(0) = 6: Problem 27 Problem List (1 point) Evaluate the integral p T/3 -9 In(tan(x)), 57/4 sin(x) cos(x) 6: Problem 29 Previous Problem Problem List Next Problem (1 point) Find the area of the region enclosed between f(x) = x2 – 3x + 8 and g(x) = 2x2 – x. Area = (Note: The graph above represents...