Recall that, for all c, = n=0 cos(x) = § 4 (-1)",21 (2n)! and sin(x) =...
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
Find all solutions to cos(4.c) - cos(2x) = sin(3.c) on 0 < x < 21 = Preview Enter a list of mathematical expressions (more..] Give your answers as a list separated by commas
1. Expand the following functions in terms of the orthogonal basis {1, sin 2nr. cos 2n on the interval (0, 1): n E Z, n > 0} 2. Expand the functions in problem i în terms of the basis {sin n z n є z,n > 0} on the interval (0, 1).
1. Expand the following functions in terms of the orthogonal basis {1, sin 2nr. cos 2n on the interval (0, 1): n E Z, n > 0} 2....
please show all work
1: Let 0 << 27, and set A= I cos(0) co -sin(0) 1 | sin(@) cos(0) . (a) Recall that fa(4) denotes the characteristic polynomial for A. Show that faa) = (1 - cos(O))2 + sin(0). (b) Using part (a) show that A has no eigenvalues if is not equal to 0 or . [ 2 -2 0 0 1 1 -1 0 0 2: Set B= 10 0 3 -4 0 0 2 -3 (a)...
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. (b) [20 pts] By using Stokes’ Theorem, evaluate the line integral| vi F. dr where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
Question 9 Find all solutions to the equation in the interval [0, 2n). sin 2x - sin 4x = 0 Your answer: O O 51 71 I, 31 111 z' ' ä 'ö' ' ő 31 1171 Oo, ma Clear answer Question 10 Find all solutions to the equation in the interval [0, 21). cos 4x - cos 2x = 0 Your answer: o o, 110 TT 51 71 31 6' 2' O No solution Clear answer Question 11 Rewrite...
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
#1 please and the
answer should be in the form of a piecewise function
(2n 1)2nn! 2 V2T n=0 Since this is an alternating series (because the parity on the power on x means that will always have the same sign as r), then we can always use the estimates on alternating series which are quite strong to compute values of this sum Problems 1.)Find the probability density function for the random variable representing picking a random real number between...
W60. Compute (sin x + cos x)(4 – 2 sin 2x – sin? 2x)e" dx sin 2x where = 6 (0,7) Mihály Be Pirkulyiev Rovsen W38. Let (an)n be a sequence, given by the recurrence: man+1 + (m - 2) an an-1 = 0 where me R is a parameter and the first two terms of (an), are fixed known real numbers. Find me R, so that lim an = 0 n-00 Tad