3. (a) The hyperbolic sine function is defined as follows: e" – e¯* sinh a = Why would we get a loss-of-significance error when evaluating sinh a for a close to 0? (b) Use 3rd degree Taylor polynomials with remainder to rewrite sinh a in a way where we would not get a loss-of-significance error. (c) Bound the error in. the approximation on the interval -1 S IŚ1.

Q: EX: - Derermine expoentail fourier series of X(t)=exp(2t) for -1<t<1 and has period of 2

A: Find the attachment for the solution.

Q: - Find the extrema of the function S(x)= 5 sin(2x) – 2x² – 4x - - Using Newton's method initial…

A:

Q: If pN(x) is the polynomial of degree N which interpolates f(x) cos(3x) at N+ 1 uniformly spaced…

A:

Q: 0.7 In this problem you will approximate the value of cos 5x dx. Find the fourth-order Taylor…

A: To find the fourth-order Taylor polynomial

Q: Approximate cos(x) for /x/< T/4 using Taylor Series (polynomial) with a true error of no greater…

A: Please check step 2 for the solution.!

Q: 4.Find the temperature T (x, t) in an infinite bar if the initial temperature is 4 for |x|3. Solve…

A: Sol

Q: 21 Date... w******** Q. Find the Fourier Series od (x) = X -즐 <x<플

A:

Q: 2- Find the positive root of f(x) = xe" - cos(x) with an error tolerance g=0.005% by using %3D a)…

A:

Q: Let f (θ) = 2 sin 2θ + sin 4θ. (a) Show that θ is a critical point if cos 4θ = −cos 2θ. (b) Show,…

A: “Hey, since there are multiple sub-parts posted, we will answer first 3 sub-parts. If you want any…

Q: Given: f(x) = 5sinx for -2pi <x<-pi/2 = 4 for x=-pi/2 =x^2 for -pi/2 < x< 2 =8cosx for 2<x< pi =4x…

A:

Q: Find the Taylor polynomial of degree 4 for cos(x), for æ near o: P4(x) = 1-x^2/2+x^4/24 Approximate…

A:

Q: Consider the IVP: x" + 4tx = 0, x(0) : - 1, x'(0) - 3 Using the Euler method with a time step of At…

A: Given, x''+4tx=0, x0=-1, x'0=-3, ∆t=0.5 Now, by Euler's method xn+1=xn+hpn=xn+∆tpnAnd,…

Q: Obtain a Fourier cosine series extension of function f(x) = e² – 1 which is continuous on the…

A: Given function is, fx=ex-1, 0≤x≤1 Part(i): For Fourier cosine series fx will be extended to a even…

Q: Q1: Find with sketch the Fourier coefficients and Fourier series of the function f(x) defined by…

A:

Q: Consider the following. S2x, 0sx < 1, sine series, period 4 f(x) (2, 1sx < 2; (a) Find the required…

A:

Q: (1) The coefficients (b, ) of the Fourier series of the function f(x)=|sin x; -7<x<7, is

A:

Q: TT The 3rd degree Taylor polynomial for cos(x) centered at a = is given by, -(*-플) 공 (*-플)" + R3o).…

A:

Q: 1/2 e an upper bound for the error in using a Taylor polynomial of degree 3 to approximate dt. You…

A:

Q: Q1: Find with sketch the Fourier coefficients and Fourier series of the function f(x) defined by…

A: Introduction: A Fourier series is a sum of sine and cosine waves that represents a periodic…

Q: 1. Find the maximum of the function: f (x) = 4sinx (1+ cosx ) a. Using Golden Section Search with…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 1. Suggest ways to avoid loss of significance in these calculations. (a) √√x4+4-2 (b) ln(x+√x² +1)…

A:

Q: = In(2- sin z) with Given sin z + e -2 0. Using the rearrangement z z0 = 0.5. what is the value of…

A: The fixed point iteration method is a step-by-step method to find the approximate solution of the…

Q: 4. Find the half-range Fourier cosine series for the function f(x)=sin-x in the range 0<x<n Sketch…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. Determine the positive root of f (x) = x³ + 2x – 2 = 0 using the Newton- Raphson method and an…

A: Here f(x) = x3 + 2x - 2 ∴ f′(x) = 3x2 + 2x0 = 0

Q: 7. (a) Use Newton's method ONCE with an initial guess of ro = 0.1 to find an approxi- mation to the…

A:

Q: 8. Find the exponential Fourier Series for the function f(t) = 2t .............. - 2 = jnm (2 fm)…

A: Given that, ft=e2t   -1&lt;t&lt;1 Find the exponential Fourier series for the given function. As we…

Q: Q 3: Show that the Fourier series for the periodic function of period 2n defined by O when - I < e <…

A:

Q: 10. Does there exist a harmonic function in z| < 1 taking the value 1 everywhere on |2| = 1? Is your…

A:

Q: 1. Find the trigonometric Fourier Series of the function defined by : filx)= x+# if (X...…... D -2…

A:

Q: Determine the following values for the nth partial sum of the Fourier Series of the given function:…

A:

Q: 5. One of the popular 3-point numerical differentiation formula is given by -3f(xo) + 4f(co +h) -…

A:

Q: (a) The hyperbolic sine function is defined as follows: e² – e- sinh = Why would we get a…

A:

Q: Compute the Fourier sine coefficients for f(x). • bn = (-4/(n^2pi^2))(3pincos(3pin/4)-4sin(3pin/4))…

A: Given function is f(x)=x   for 0≤x≤60   for 0≤x≤8 hence Fourier sine series is ∑n=0∞bnsinnπx8 and…

Q: Q3// Expand f(x) : = -x - Tt , - n< x< 0 in a half range sine series and Find its Fourier series

A:

Q: 1. Problem. Express the function f(x) e"/L (for 0 < x <L and assumed to be periodic with period L)…

A: Given:- Express the function f(x) = ex/L (for 0 ≤ x ≤ L and assumed to be periodic with period L) as…

Q: 5. Find the term representing the third har- monic for the periodic function of period 27 given by:…

A:

Q: Determine the Fourier series for the periodic function. f(x) = Problem 2 -2, when -π <x<0 +2, when…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Part 1 of 2 Find the Taylor polynomial T3(x) for f(x) = cos(x) centered at r = . o(--) -(--)*+ (--)"…

A:

Q: The Bessel function of order 0 is represented by the series J0(x) = sum of x=∞ and n=0. (−1)^…

A: J_0(x)=-J_1(x)

Q: The 4" degree Taylor polynomial for sin(x) centered at a = . is given by the following. 6 V3 V3 X -…

A: Solution: Rewrite as x=39 39∘=30∘+9∘=π6+π20

Q: Q1// Expand f(x) = sin(x + n) , 0<x<; in a half range sine series

A:

Q: 30. (a) Expand in a Fourier series f(x) cos z, 0<<, if the period is r: and (8) compare with the…

A: According to guidelines,  I can answer only 1 question which is in first .

Q: 5. Find the term representing the third har- monic for the periodic function of period 27 given by:…

A:

Q: Q4: A. Find The Fourier series for the function defined by 2k * (x) if 0 <x <; f (x) = 2kx Tl-x) if…

A:

Q: The 4th degree Taylor polynomial for sin(x) centered at a = is given by 2 V3 sin(x) = ? ) + (* -)* +…

A: We know that, 39 degrees = (39) . (pi/180) = (13 pi)/60 radians Given that the Taylor polynomial for…

Q: A string stretched between the two points (0, 0) and (2, 0) is plucked by displacing the string h…

A: Evaluate: bn=h∫01xsinnπx2dx+h∫12-x+2sinnπx2dx

Q: Find the first four nonzero terms of the Taylor series about 0 for the function f(x) = √√1 + x…

A:

Q: Let pn (2) be the Taylor polynomial of degree n of f(x) = cos x about Problem 2. a=0. How large…

A: The given function is: fx=cos x The remainder for the Taylor series about x=a is determined as…

Q: 3. The function f(x) = xe=^(-x) has a unique root x = 0.(a) Compute several iterations of the…

A: The given function,