Suppose Theta belongs to Aut(Zn) and a is relatively prime to n.  If Theta(a)=b, determine a formula for Theta(x).

Q: Integrate the following with respect to t 20 cos30

A: Solution:To integratelet I=∫2θ cos3θ dθFormula:∫ cos aθ dθ=sin aθa+C ∫ sin θ dθ=-cos…

Q: Find 7'(t), given ř(t) = ( – 4cos( – 5t), 3 sin( – 5t), e*). - - F (t) =

A: Solve the following

Q: 5. Find a function u(r, 8) that is harmonic outside the unit disk, equals f(0) = 2 sin(30) + 4 cos…

A: In the given problem we used the fact that f is harmonic on the unit circle, and using the…

Q: Locate the first positive root of: f(0) = sin(0) + cos(1+ 02) – 1 Where 0 is in radians. Use four…

A:

Q: 1 Find a formula in the form y = A sin(Bx)+ C which produces the following graphs: (270°, 1) 90°…

A:

Q: Find the maclauin's sesies for y= cos(%)

A: y=fx=cosx2 Differentiating with respect to x, we get f'x=-12sinx2 Again differentiating with respect…

Q: The approximation of 1 = f*cos (x5)dx using composite Simpson's rule with n = 3 is: 0.5412 O None of…

A: Option A is correct

Q: An RCL circuit connected in series with a resistance of 4 ohms, a capacitor of 1/26 farad, and an…

A: This question is about application differential equation.

Q: Given the ODE (cscy)dx + (cos²x)dy = 0. A one-parameter solution of it is: O cosy + tanx = c siny =…

A:

Q: A-Show that S 1, L{cos at} s2+a²

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use symmetry to evaluate the followingintegrals.

A:

Q: Suppose z and y are funetions of time and satisfy the formula e sin y = In y + tan dy Write a…

A: Solution:- differentiate with respect to t.

Q: Q.1- For this signal, Find the complex exponential Fourier series. X(t) = 5 cos 30Tt - 8 sin? 20Tt…

A: Consider the given equation:

Q: The function f(x) satisfies the hypotheses of the Mean Value Theorem on %3D cos(z)+1 Select one: a.…

A:

Q: Show that the functions have local extremevalues at the given values of θ, and say which kind of…

A: Consider the given function is h(θ)=3cosθ2 for the range 0≤θ≤2π. The first derivative of the…

Q: 1) Find the fundamental period of the function u + v, if any, by examining whether the functions u…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: An RCL circuit connected in series with a resistance of 4 ohms, a capacitor of 1/26 farad, and an…

A:

Q: Locate the first non trivial root of sin(x)=x2 where x is in radians. Use a graphical technique and…

A: Use the following MATLAB code to plot the given function f(x)=sin x-x2=0 clear;clc;

Q: B Integrate the following. * cos x' dx 2 a.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the z-values of cos i = e²

A: Given

Q: The periodic function with L=2 is presented as f(x)= 0 if -1<x<0 and f(x)= x if 0<x<1. Find the…

A:

Q: In  the given equation as follows , use Taylor’s Theorem to obtain an upper bound for the error of…

A: Approximation is a result that is near, not exactly, but almost accurate. To find the simpler value…

Q: 10. Compute the following: »TT/4 (a) COS dx 3 (b) dax

A: Part (a)-Given:

Q: Use symmetry to evaluate the followingintegrals.

A: We have to find definite  integral using symmetry.

Q: Show that the formula gives the decomposition odd function. e* = cosh(x) + sinh(x) of the function…

A: Even function: Let fx is the real-valued function, where x is the real number, then, fx is an even…

Q: Find the exact lanth of the 4=1n (sec(x)), Odyct3

A:

Q: Prove: L{cos at} = s2+ a?

A: We will prove the given statement.

Q: 3) Find the general solutions only of the following higher order ODE by method of undetermined…

A:

Q: Find 7'(t), given 7(t) - 4e 2t (3 sin(2t), ,4 cos(4t)). F'(t) =

A:

Q: The amplitude A and period T of f(x)=5sin(4x) are..................... and ....................

A:

Q: O Find the inde frinite in tgal 曲 A cos (2¢) df

A:

Q: From the equation, f(θ)=sinθcos2θ-(cot θ / θ) +1, what is/are the critical points?

A: Consider the equation

Q: Suppose that f(t) is the half-wave rectification of sin kt, shown in Fig. 7.5.16. Show that L{f(!)}…

A:

Q: Plot the following signals in the time range 0sts 30 sec, and determine if these signals are…

A: Solution a: Given x[n]=sin10n Comparing with sinωn So we have ω=10 Since we know ω=2πf⇒10=2πf⇒f=5π…

Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

A:

Q: Compute the following. S3x?cos(x³)dx

A:

Q: Find the Wronskian of the following set of functions 1. {sin 3x, cos 3x}

A:

Q: .Inside the outer loop of the limason r 1-2 cos e

A: Given that r=1-2cos(theta) We have to find area.

Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: /Prove that the value of cos()dz, when z = T + 2i is e + e-1

A: Complex integration of the function

Q: See image below....

A:

Q: Consider the image attached of the functions f(x) = 12*cos(2x+1)-6 and g(x) = -1. Set f(x) = g(x)…

A: Given that, the functions are fx=12cos2x+1-6 and gx=-1. Equate the functions to find the solution x…

Q: Consider f(x)=xsinx If f(x) is periodic what is the fundamental period?? If f(x) is not periodic,…

A: The function is periodic if f(x+T)=f(x) here f(x+T)=x+Tsin(x+T) which is not equal to f(x) also ,…

Q: Given the following integral of a trigonometric function raised to an odd power dx and its…

A: Given that  The integral is  To find the value of integral by using the trigonometric substitution

Q: Find a closet rank-1 approximation in the (2 cos 0 - sin norm to A = sin 0 cos e

A: Consider the provided question, The l2 norm or Forbenius norm(FN) is the square root of the sum of…

Q: Find the half-range cos and sin expansion of: 0sts p/2) p/2 stsp) f(t) = %3D lo

A:

Q: Find the exact values of s in the given interval that satisfy the given condition. [0, 2n); cos s=-

A:

Q: 1) Find the fundamental period of the functionu +v, if any, by examining whether the functions u (t)…

A: All trigonometric functions are periodic. To find if ut=sin2t is periodic: Express it in terms of…

Q: Find a function u(r, 8) that is harmonic outside the unit disk, equals f(0) = 2 sin(30) + 4 cos (50)…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…