With the calculus of residues show that (2n)! cos2n 6 do = 1720 (91) 2 (2n...
Complex analysis and using the
cauchys residues theorem solve the integral .
i know how to do it using calculus so do not do it using
calculus please
sech x dz =-. Hint: Consider the rectangle with corners 14.. Show that 2 0
sech x dz =-. Hint: Consider the rectangle with corners 14.. Show that 2 0
10. Let and consider approximating its average value on the interval (0,2) given by the integral 4-2 dx. 0 (a) Use Calculus to show that the the exact answer is π/2. (Hint: You may want to substitute 2 sin , and later use the trignometric identify cos(20)-1-2 cos2 θ). (b) Assume r is uniformly distributed in (0,2). What is the expected value, E f ()] How is the formula for expected value related to the expression given by expression in...
Show that * В, ze:2 + e-z/2 2 e32 - Σ ܂ܙܐܕ݂܂ 2/2 n=0 (2n)! In this question, B is a Bernoulli number Replace z by 2niz to show that 00 Az cot az = (-1) Š (21)2 B2nza R=0 (2n)!
2. Caleulate the residues at the indicated poles coS 2 a)- z=0; il , 2 2 sin z (c) 따가, 1+22)22j.
2. Caleulate the residues at the indicated poles coS 2 a)- z=0; il , 2 2 sin z (c) 따가, 1+22)22j.
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....
Vector / Complex Calculus
6. Calculate the integrals of cos(z)/z" and sin(x)/2" over the unit circle, where n is a positive integer.
Exercise 12: Residues and real integrals (a) [6+4 points) Compute the residues for all isolated singularities of the following functions (i) f(2)== (2-) tan(2), (i) 9(2):= z2 sin () (b) (4+6+5 points) Compute (using the Residue theorem) (1) cos(72) ( d, A3 := {z € C:<3), 243 := {Z EC: | = 3}, 34, (2-1)(2 + 2)2(2-4) : 43 € C:21 <3}, po 12 To (x2 + 4)2 da, 24 2 + 4 cosat. J 5 + 4 sin(t)
This is calculus based physics. SHOW ALL WORK
Equations:
dar -1 arctan (z/a) (a2 r2) cos(a y) os(z)cos (y) sin(z)sin(y) COS 1 cos(2r B. ds Au0Ienc E. dA. E. dA Wenc dB 1 da dEy 4Teo r2 4TTE YAV 0 For a closed loop out 27a. IR AVe dt EA BA x BA BB BA UBA x E Ex B
The value of cos(x) is evaluated as follows: cos(x)=1- x^2/2!+ x^4/4!- x^6/6!+ x^8/8!+⋯+ x^2n/((2n)!) Where n is related to the accuracy level required for cos(x). Write a C++ program that asks the user to input n and x and then the program will evaluate cos(x) up to the 2n terms.
please solve 2 to 6 with details
Advanced Calculus: HW 3 (1) Suppose that a E R has the following property: for all n e N, a < Prove that a<0. (2) Prove that the set of integers Z is not dense in R (3) Let A = {xeQ: >0}. Determine whether A is dense in R, and justify your answer with a proof. (4) Find the supremum of the set A= {a e Q: <5} (5) Let a >...