Question 3 Find the Taylor polynomial P11(x) centered at x = 0 for the function f(x) = 4x sin(2x2). а) 4 2х — 4 11 + 15 16 16 b) O 8x3. 3 + 16 16 c) O2x + x' 15+1 d) O 8x + *' + 15*" 4 .7 1 .11 16 16 e) O8x - x' + 3

Q: 3. Let d 2 2 and let P(z) = ao + ajz + ... + a4z“, ad # 0 be a polynomial with real coefficients…

A: Please note that I am able to see only one part, namely part (a). So, I can solve only part (a) for…

Q: Q4) Find Fourier transform of the functions: 1)f(x)= nxl, x π 3)f(x)=xe-x1, x ER 2)f(x) = 4)f(x) =…

A:

Q: Express x^8-x over 2[x] and over F2[x] as a product of irreducible

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Q: tan (3r) dr = a tan(3x) – In(v1 + 9x²) +C 3 a tan (3x) + In(v1+9r²) 3. e tan '(3x) In(v1 - 9x² +C a…

A: We know that, from basic integral formula ∫tan-1x=xtan-1x-12log1+x2+C          ⋯⋯1 We have, the…

Q: 18. Find a monic polynomial of least degree in R[x] that has 4i-1 and -3 as roots. write the powers…

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Q: Solve if w be cube root of unity then (1+w)(1+w^2)(1+w^4)(1+w^8).....2nfactor=1

A:

Q: 3 a2 Calculate the integral: da (*- 9)2 (x+ 9)

A: ∫3x2x-92x+9dx=3·∫x2x-92x+9dxTaking partial fraction…

Q: (a) Show that the polynomial of degree 3 is differentiable in the complex plane, also find f'(z).…

A: For part (a): It is required to show that the polynomial of degree 3 is differentiable in the…

Q: for 0<x < 3, Let f(2) = {- (z – 3) (x – 3) for 3 < x < 6. Compute the Fourier cosine coefficients…

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

Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

A:

Q: (d) (27+5)(2- i)|=/3 12z +5|. %3D

A: Solution D: We have to prove (2z¯+5)(2-i)=3(2z+5) L.H.S. Let z=x+iy So z¯=x-iy therefore…

Q: Part (b) 5e Evaluate -dz by residue theorem, where C is the contour |z| = 2 6z4 +30z3

A:

Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: f(x) = e-5x, a = 0 OA) 1-5x + 2²-125³ 2 6 OB) 1-5x + 22²-15³ 2 3 OC) 1-5x + 2²-1¹ 25x2.125x3 18 OD)…

A: fx=e-5x Taylor polynomial  at x=a=0⇒fx=f00!x0+f'01!x1+f''02!x2+f'''03!x3+.....

Q: consider the degree 4 LFSR given by polynomial p(x)=x^4+x^2+1. What kind of polynomial is this…

A: The given polynomial p(x)=x^4+x^2+1 With 4 LFSR.

Q: Use synthetic division to solve: I1) -74) + (x - 8) 13) n' + 7n² + 14n + 3) +la + 2) 14) - 10p + 20p…

A: Here we solve the problem using synthetic method. Note: it's Bartleby policy there is only one…

Q: A periodic function f(x) = g(x+2x) f (x +27) us given by x+ π -TULX LO π-x, 0≤xs t 2 a) Sketch f(x)…

A:

Q: A Moving to another question will save this response. Question 10 "The product of a negative real…

A: Let us assume a negative real number x. So, x&lt;0 And a positive real number y. So, y&gt;0

Q: if the Legendre polynomials P.(x) = -1 then: Find 1) ,x* P,(2) dx 2)P'(-1) A) L P.) dx = and P,(1) -…

A:

Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

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Q: Q8) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant…

A: Given: Roots of the characteristic equation of a homogeneous ODE with constant coefficients are…

Q: A 14) E (2+¹)= (a) {Σ##s (n + 1) (c) a and b a b O C do 15) For the Chebeshev polynomial of the…

A: We will use properties of combinatorial series

Q: 2) Prove that: d? L„0) = n;(n – 1) %3D dx²

A: Consider the given information: Let Laguerre polynomial is given by, Lnx=∑k=0n(-1)kk!nkxk…

Q: None

A: Given, a)   f(x)=(x-2)2  b)   f(x)=(x-1)(x+1)

Q: k ak ak a-1,a +1 (-1)* 1/½(-1)*+1 kak 4), a +1 a- (ak + b)(n) (ak+b)(n+1) a(n+1)

A: ∆ak= ak+1-ak      = ak(a-1) therefore anti difference of ak=ak/(a-1)

Q: QUESTION 1 Find (i) the constant term. (ii) the coefficient of r and (ii) the degree of the…

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Q: Q5) Find the root of f(x)= 5 sin(x) + ex² by using bisection method take a= -1.25 and b= -1.0 for…

A: Given, fx=5sinx+ex2. Here, a=-1.25b=-1.0 Now,…

Q: If you let R=Z[x]and I = (x^2 -2) be the principal ideal generated by f(x) = (x^2 -2). If r=2x + I…

A: The objective of the question is to prove that r^2=8 + I in the quotient ring R/I, where R is the…

Q: If you let R=Z[x] and I = (x^2 -2) be the principal ideal generated by f(x) = (x^2 -2). If r=(2x +…

A:

Q: Q6) (a) Prove that Fourier cosine transform of f(x) = cos(x), 1 sin 3(p-1), sin 3(p+1) p-1 p+1 +…

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Q: Find the second Lagrange înterpolation polynomial that rn tercepts flx)= x²+xe*+sinx at points xo=0,…

A: We have to find the second-order Lagrange interpolation polynomial that interpolates fx=x2+xex+sinx…

Q: 1. Differentiate. All the asnwer must be brought to their simplest factored form possible AND in…

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Q: 11. The Hermite polynomials, H,„(x), satisfy the following: į. = Se-**H„(x)Hm(x) dx = \T2"n! 8,m:…

A: To prove: ∫-∞∞xe-x2HnxHmxdx=π2n-1n![δm,n-1+2n+1δm,n+1] Proof: Take the LHS ∫-∞∞xe-x2HnxHmxdx and…

Q: Find the equation in red in the same way as the equation in the second picture(I need same by…

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Q: Find all the real zeros of the polynomial P(r) r'+6r+7x-4.

A: Given,          The polynomial is Px=x3+6x2+7x-4 .

Q: Exercies: 1) Express the polynomial xr + 2x? – 5x + 2 in a series of Laguerre polynomials. 2) Prove…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…