4. Consider the complex number w = 3cis (5). For which value(s) of k is x – wa factor of the polynomial f(x) = x³ – -k?

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Q: Find the nth Maclaurin polynomial for the function. f(x) = 4 coS TX, n= 4 %3D 3 4 4 IL X 24 3 2.2…

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Q: 6. Find the nth degree polynomial that satisfies the given conditions. (R__S_ n = 4, and 2 + 3i are…

A: Given: - The conditions are, n=4, 13and 2+3i are zeros: f(1)=100 To find: - The nth degree…

Q: 4. Consider the complex number w = 3cis (). For which value(s) of k is z - w a factor of the…

A: We will use remainder theorem to find the value of k. Remainder theorem says that if x-a is a factor…

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Q: If L(x)=mx+b is the linearization of the cube root of 3x+1 at x=333, then b= Enter your answer as a…

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Q: Consider the problem maxx [-(x - 4)]² subject to x21. Use Thus the Kuhn-Tucker conditions to find a…

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Q: The ________ ________ ________ states that if f(x) is a polynomial of degree n (n > 0), then f(x)…

A: Consider the statement, The ________ ________ ________ states that if f(x) is a polynomial of degree…

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

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Q: .(1) t is straightforward to show that y = k-1 is a solution to the homog quation

A: Given,                yk+2 -2k+1kyk+1+ kk-1yk=0         (3.151)and       yk+2 -2k+1kyk+1+…

Q: 13R Q2 Put the complex number Z = 2e in the "Cartesian" form Z a+ bi where a, b E R.

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Q: 1. Using the points xo = 1 , x1 = 1.6, and x2 = 2.5, find the Lagrange interpolating polynomial that…

A: We find the Lagrange interpreting polynomial using the given points and that fits the function 2/x2.

Q: Use the inverse form of the first translation theorem to determine the power of e. 2! %3D (S-5)° -5t…

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Q: h 1/27 (5 fn+1 +8fn - fn-1) Xn+1 = Xn + Discuss its local truncation error O(hP+1)

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

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Q: 4. following is correct? A. B. C. Let p = a + jb, b > 0 be the complex root of the denominator of…

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Q: Find the third Taylor polynomial for f(x) = sin(2x), expanded about c = n/6. %3D

A: Given: fx=sin2x and c=π6 To find the third Taylor polynomial of the given function. The formula for…

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…

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Q: 2. Find the Maclaurin polynomial of f (x) = cos x.

A: Using maclaurian series of polynomials,

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Q: 3. Use the third degree Maclaurin polynomial of f to approximate th value of 0.2 ln(1.1), give your…

A: Macluarin polynomial of the function

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Q: 7. (a) Find a cubic polynomial, q(x), such that q(0) = cos 0, q = COS = coS q (T) = cos ㅠ. 3 3 (b)…

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Q: Solve the following Higher Order Non-homogenous DE using Methods of undetermined coefficients…

A: Given,y'' -2y' +y=3x+2A second order linear, non-homogeneous ODE has the form of   ay''+by'+cy=gxThe…

Q: B. Write down the Taylor polynomial of degree 5 for the function f(x) = x³ about x = 8. Use it to…

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Q: b) Show that P1(cos(0)) and P2(cos(0)) are orthogonal to each other, P, and P2 being Legendre…

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Q: 5. (a) Find the real constants P, Q, R, for which 3 P Qx + R x2 – x + 1° x3 + 1 x + 1 | Show that V3…

A: 5(a)  3 / (x3+1) = P/(x+1) + (Qx+R)/(x2-x+1) ......(1) Now, 3/ (x+1)(x2-x+1) = P/(x+1) +…

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A: According to the given information, consider

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Q: Let z1 = 4 + 4i and z2 = 4 – 5i. Find (in the form x + iy): (5z1 + 4z2)? +i i i

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Q: a. Show that if Then z = z. b. Evaluate all the roots of the Equation: z* + 16 = 0

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Q: t is known that the polynomial p(x) = 2- (r+ 1) + x(x+ 1) – 2x(r + 1)(r – 1) interpolates the first…

A: Given:- p(x)=2-(x+1)+x(x+1)-2x(x+1)(x-)  interpolates the first four points of the table. x -1 0…

Q: 350. Prove that the function w(z), expressing the roots of the equa- tion 3w- 25w + 60w – z = 0 in…

A: We have to prove the function wz, expressing the roots of the equation: 3w5-25w3+60w-z=0 in terms of…

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Q: Consider the following quadratic f(x)=x2−11x+1f(x)=x2−11x+1 with the roots αα and ββ. Suppose the…

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Q: 4. Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of %3D a+bi.

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Q: Find the Maclaurin polynomial p3 for f(x) = cos( 중).

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Q: 2. Find the 5th degree Maclaurin polynomial of f(x) = e-".

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Q: The characteristic of Z5[x]/ is

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Q: 3. Use a divided difference table to find the Hermite polynomial approximation of a sin(2x-3+1 which…

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Q: If L(x)=mx+b is the linearization of the cube root of 3x+1 at x-333, then b= Enter your answer as a…

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Q: Using the two points (x,y) and (x₁,51) to find Lagrange interpolating polynomial, L.(x1) is always…

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Q: a) Show that u(x,y) = x3 – 3xy2 + 3x2 – 3y2 is harmonic and find its harmonic conjugate

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