


у Give all necessary dimensions yourself F=5000 N and Material=> E295 There is torsional stress in...
Graph the function f ro -2<x<0 f(x) = +1 O 5x<1 1 1 sx<2 Find the Fourier series of fon the given interval. Give the number to which the Fourier series converges
B. Find the Laplace transform of the following functions. 1. f(t) = {" where n is a positive integer, 2. f(t) = { • 10<t< 0 <t< 3. f(t) = { t 0<t<1 2-t i<t<2 0 2<t<
Let F(x,y,z) = <2y2z, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative, find a function f such that F = Vf and f(1,2,1)= 8. (b) Using the result of part(a), evaluate the line integral of F along the following curve C from (0, 0, 0) to (3.9, 1.4, 2.6). y2 + x4z3 + 2xy(x3 + y4 + 24)1/3 = K ; K is a constant Answer: Next page
Exercise 1: Find Laplace transform of the following: 1. f(t) = 3t2 – Sin4t. 2. g(t) =3(t – 1) + e-t. 3. k(t) = { 2+2, t< 2 t> 2
Exercise 1: Find Laplace transform of the following: 1. f(t) = 3t2 – Sin4t. 2. g(t) =3(t – 1) + e-t. 3. k(t) = { 2+2, t< 2 t> 2
Let F(XYZ) = <2y27, 4xyz, 2xy2> be a vector field. (a) Knowing that F is conservative, find a function f such that F = vfand f(1,2,1) = 8. (b) Using the result of part(a), evaluate the line integral of F along the following curve C from (0,0,0) to (3.9, 1.8, 2.3). y2 + x4z2 + 2x4(x3 + y2 + 24)1/2 = K Kis a constant .- Answer:
Need help please the steps, thanks.
K=2
(i) Let 0 < x < 1; et f(x) x tk, 1<x<2, } the Fourier series at x = 1. مر and let f(x) be 2-periodic. Find the value of
1. A continuous random variable has probability density function f(x) = 2x for all 0 < x < 1 and f(x) = 0 for all other 2. Find Prli <x< 1. O 1 16 O OP O . O 1
[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x + 2y) 0 for 0 < x < 2, 0 < y < 1 elsewhere (a) Find k (b) Find the Marginal density of Y. (c) Find E(Y) (d) Find marginal density X. (e) Find the probability, P(X < 1.3). (f) Evaluate fı(x|y); (g) Evaluate fi(x|(0.75))
4. Use the power series representaion f(t) = In(1 - 1) =- for -1 <<1, k=1 to find the power series representation for the following function(centered at 0). Give the interval of convergence of the new series. p(r) = 2.r" ln(1-2) 5. Find the power series representation for g centered at 0 by differentiating or integrating the power series of f(perhaps more than once). Give the interval of convergence for the resulting series. 1 using (3) 1-