Q5. (a) i. Prove that the inverse transformation W = = Z transforms the straight line ax + by = 0 is a straight line through the origin. ii. Show that the image of the hyperbola x² - y² = 1 is the transiscate p² = cos2p. (b) Obtain the Taylor's series to represent the function |Z| < 2. z²-1 (z+2)(Z+3) in the region

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A: Given,                 f(x)=cos(x), at x0=0. To find the 5th Taylor polynomial p5  for f(x)…

Q: 4. Sketch several periods of the following function: f (x) 0,- pi<x<0;1,0<x<pi/2;0,pi/2<x<pi Expand…

A: Given the function is fx=0-π&lt;x&lt;010&lt;x&lt;π20π2&lt;x&lt;π

Q: ) Obtain the Taylor's series to represent the function |z| < 2. z²-1 (z+2)(Z+3) in the region

A: Given function as z2-1z+2z+3

Q: 39.. Find the Taylor polynomials (centred at zero) of degrees (a) 2, (b) 4, (c) 6, (d) 8. 1 f(x) =…

A: We know that Taylor Expansion : f(x)=11+x=1-x+x2-x3+x4-.........∞.

Q: Compute the coefficients of the Fourier series for the 2-periodic function f(t) = 9+2 cos(2πt) + 5…

A: Since the given function represents Fourier series, therefore the required coefficients are…

Q: 8. Find the exponential Fouvier series for the function f..(t)... f(t) = 2t 1.f.t.<..... *** ·2=jn π…

A:

Q: c) The divergence of F(x) = (2x³y)i + (y2e?)j – (5x cos z )k is d) The inverse Laplace transform of…

A:

Q: 5. (a) Find the Taylor polynomial T2(x) of f(x) = V (= x'/3) centered at a = 1. %3D (b) Let T2(x) be…

A: f(x)=x3To Find:a) Taylor polynomial of f(x) centered at a=1b) Use Lagrange's error bound to justify…

Q: x(t) x(t) Sak 1 a = sin(k -T;)/kn -T T=6 Obtain the Fourier Series coefficients of the sign z (t)…

A: Given graph is By the graph we can define the function Z(t) as Z(t)=t,    0&lt;t≤11,…

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A: Given function is fx=e2x+cosx.

Q: c) For a periodic function y(t) with period T, its Fourier series may be represented in complex form…

A:

Q: Find a + b + c + d + e. The Fourier series of the function f(t) = f(t) == 1 π 4 플 n=1,3,5,... ;0≤ t…

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Q: Find the Taylor polynomial with 4 nonzero terms about x = 0 for the function f(x) = ferª dx, f(0) =…

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Q: Exer. 81-82: When computations are carried out on a cal- culator, the quadratic formula will not…

A: The first formula is denoted as x=-b±b2-4ac2a and the second formula is denoted as x=2c-b∓b2-4ac. We…

Q: 1) Find the n"-order Taylor polynomials of the given function centered at the given point for n = 2…

A: Solve the following

Q: 13. Let the function f (x) be 2n-periodic and suppose it is represented by the Fourier series: f (x)…

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Q: 6. Express the inverse Laplace transform of the function shown to the right via the residue method.…

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Q: Find the Taylor polynomial T,(x) for the function f centered at the number a. f(x) = 7 tan-(x), a =…

A: Given:

Q: (27) Consider the piecewise function f : [-L, L] –→ R given by Ja + L, if – L <x < 0 f(x) : x*, if 0…

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Q: Calculate the Fourier series for the function f(r) = 6(r –- 1) – 6(r+ 1) when -2 <aS2 and is…

A: The function is odd so there will be no constant and cosine terms.  The Fourier series will be:

Q: Find the 3rd degree Taylor polynomial T3 (x) centered at a 2 for the function f(x) = e"/5 e2/5 (x-…

A:

Q: 12. Letfbet the function given by ƒ(x) = cos(3x + 2) and let P(x) be the fourth-degree Taylor…

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Q: f(2) = {; -1, -n<x < 0, 1, 0 <x< n

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Q: Q9. (a) (i) Calculate (2 + i√5)(√5 - i). (ii) Hence verify that (√5 - i) is a root of the equ

A: (a) The given expression is 2+i55-i Multiply the terms in the given expression…

Q: 4. that has the asymptotes x 7 and y = 6. Write an equation for the translation of y = 4 Oy=ー+7 -6 4…

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Q: a) Calculate the first order taylor polynomial T1(x) about x =8, and use it to approximate…

A: We have to approximate the Taylor polynomial about

Q: 5) Find the Inverse Transform of the Partial Fraction: 5s C-¹ ( 258,+12) L-1 s

A:

Q: Calculate the third Taylor Polynomial T, centered at a= 4 for the function f (x) = \x+5.

A:

Q: Question 3 Find the Taylor polynomial P11(x) centered at x = 0 for the function f(x) = 4x sin(2x2).…

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Q: 2) Find the third degree Taylor polynomial centered at c= for the function. 6 f(x) = sinx

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Q: Name 1. The point (-1, 4) is reflected over the y-axis. What are the coordinates of the new point?…

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Q: f(x) = [0,-1<x<0 2,0<x< 1 Compute the coefficients by hand. Then, give the maple code used to plot…

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Q: (a) Write the Taylor polynomial of degree 6 centered at 7 for cosx. (b) Use ≈ 3.14159 and the above…

A: (a)          Let…