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

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A: To solving the system we use the Gaussian Eliminating and back substitute method

Q: 1) 2) 3) cos ¹(2) j(1-j√3)(√8+j) (1+j)(1-j√3)²

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Q: 2. Find the first four Taylor polynomials for, f(x)= In x about x=2

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Q: Q2) Find the expansion in Legendre polynomials of the functions: a) f(x)=2-x-x² x) = { 1 ) 0, b)…

A: We have to find the expansion in Legendre polynomials of the function.

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Q: 9) How many roots (zeros) does f (x) have? a) 0 b) 1 c) 2 d) 3 e) 4 10) How many extreme points does…

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Q: Find the coefficient of X^35 in the generating function (x^4+x^5+x^6+x^7+x^8)^5 (Show work and…

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Q: The best approximation of f(x) = cos(8 + x) by a Fourier polynomial of degree 1 is

A: The Fourier Polynomial of degree n is Fn(x)=a0 + ∑k=1nakcos(kx) +∑k=1nbksin(kx). Then, the Fourier…

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Q: Using Newton's interpolating polynomial of order 2, namely, bo +b,(x-x)+b,(x-x)(*-x) where x, = 0,…

A: Given:   Newton’s method for polynomial interpolation of order two is given as:…

Q: (ii) w* +1 – 8(@) TOEY 4 2.

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Q: Suppose P(z) is a polynomial satisfying • P(5) = - 5 P'(5) P"(5) = - 156 Р(3) (5) 3D — 414 305

A: Introduction: The term "polynomial" refers to a sort of expression. A mathematical statement without…

Q: x² – 4 Evaluate: A =Vx2-4+ sec-스)+C ⑥ -Vx2-4+2 sec-스)+C =V x2 – 4 – 2 sec + C (D =2Vx2-4+ sec-1스)+C…

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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 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<0 And a positive real number y. So, y>0

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

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Q: If B' is of order 2x3 and BA is order 3x4, then A is of the order T

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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: 6. Show that when 0 < |-1|< 2, (z-1)(z-3) Complex Analysis (z-1)" 2+2 =-36 z−3) ² A=0 2(z-1)

A: We use substitution and Laurent series expansion.

Q: If f(Z) = cos (3z2) then the simplify form of f(2) is: A) f(z) = i log(3z² + iv9z+ – 1 B) f(Z) = -i…

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Q: 1. Find the Newton-Hermite interpolation polynomial for f(x) with f(1) = 8, f'(1) = 16, ƒ(3) = 16,…

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

Q: lef f(x) = x-2₁ g(x) = ³√x₁ h(x)=x4, and j(x) = 4x, Express oach of the function. given below one or…

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Q: Question 2 Find the Taylor polynomial P5(x) centered at x = 0 for the function f(x) = 5x² – 3…

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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)

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A: We have to find the Taylor second order polynomial.

Q: hd the invense transformof eack of t FX) 6x-5 FCx)=

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Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

A: Answer

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Q: Write a polynomial function of least degree with integral coefficients that has the given zeros. 23)…

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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: Integrate the function. √√36-x² dx O 18 sin O sin ¹ (-2) + x√/ 36 - x² + C +C 2 O 36x √√36-x²…

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Q: Question 5 (Show your work!) Find the coefficients of 2. r* in (r2 - (1/x))". |

A: (x²-(1/x))^n