State the domain of f g. Then find f• g, including any additional restrictions necessary on the domain of the composition. Ax) == g(x) = Jx+3 -7 D: x> -3; (f • g)(x) = Vx+3 -7 D: x2 -3; (f • g)(x) = Vx+3 O D: x - 0; (f • g)(x) = .: +3 D: x - 0; (f • g)(x) = Vx+3 -7

Q: Find the Taylor polynomial for f(x) = (x – 1) * sin(2(x – 1)), xo = 1, n = 2. F(x) ~ P2(x) = ax² +…

A: Solution

Q: Use the def'n of to test the dif ferentiability of the x=0 : ヘ人る given gn at Sx²+2x-1, x<o ○け f(x) =…

A:

Q: Find the second Lagrange interpolation polynomial that fn tercepts f(x)= x2+xe*+sînx at points xo=0,…

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Q: Show that : f(x) = x2 + x + 2 e Zg[x} is irreducible. Further, find the order of f (x).

A: Definition: 1. A polynomial f(x) ∈ ℤp[x] is said to be irreducible if and only if it has no root in…

Q: Form the interpolating polynomial of degree k that satisfies pG) (xo) = f(G) (xo) for 0<j< k.

A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

Q: (i) Construct the minimax polynomial p2 E P2 on the interval (-1,1] for the function g defined by…

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A: This is a problem of asymptotic growth.

Q: (h) Write down the Lagrange's polynomial through (xo, fo). (x1,fi), (X2, f2). Hence express 3x² +x+1…

A: Hello. Since your question has multiple parts, we will solve the first  part for you. If you want…

Q: "Let T_3(x) be the Maclaurin polynomial of f(x)=e^x. Apply the Error Bound to find the maximum value…

A: Given that f(x)=ex The maclaurin series is, ex=1+x+x22!+x33!+....+xnn! Where, T3=x44!+...+xnn!+....

Q: 1. If the third degree Taylor polynomial of f(x) centered at r = 3 is P(x) = 5 – 2(x – 3) +(x – 3)²…

A:

Q: Find the degree 3 Taylor polynomial T3 (x) of function f(x) = (-7x + 46)³/2 %3D at a = 6. T3(x) =

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Q: Show that the nth Maclaurin polynomial for f(x) = e* is Tn (x) = 1+ 2! n!

A:

Q: 4. Prove that if f(x) = aox" + a,x"-1+ ...+ an-1x = 0 has a positive root x = xo, then the equation…

A: Roll's theorem: If f is continuous function on [a, b], differentiable on (a, b) and f(a) = f(b) then…

Q: , Consider the interpolating polynomial for f(x) =x² based on th points (0,0). (1,1) and (2,8). Find…

A:

Q: The Taylor polynomial of the function f(x)= e* up to order 3 about X = 0 is given by 1- x+x²- 6 a O…

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Q: 25. Find a polynomial q e P2(R) such that p(x)(сos TTx) dx p(x)q(x) dx for every p E P2(R).

A:

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Q: For f(x) = x - 4x + 3, there exists a'c' in [1, 3], which satisfies the conditions of Rolle's…

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Q: Suppose f:N→ N has the rule f(n) = 3n² – 1. (a) Determine whether f is surjection onto N and show…

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A: on solving this we get

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Q: 1. Consider y=f(x)=sin(3x)+x² over [0, 3¤/2]. (By hand but use a calculator) a) Use the three nodes…

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A:

Q: . Suppose that f is a polynomial of degree 1 and s1, is the linear spline that interpolates f at the…

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Q: Use the second Taylor polynomial P2(x)P2(x) for f(x)=x2+ln(1+x)f(x)=x2+ln⁡(1+x) about x0=0x0=0 and…

A: P2x=f0+f'0x-0+f''0x-02f(x)=x2+ln(1+x)f(0)=0f'(x)=2x+11+xf'(0)=1f"(x)=2-1(1+x)2f"(0)=2-1=1∴P2(x)=x+x2…

Q: (c) Show that : f(x) = x2 + x + 2 e Zg[x] %3D is irreducible. Further, find the order of f (2).

A:

Q: Let f(x) = 7x2(x – 11) + 12. Find the critical points c that correspond to local minima.

A:

Q: Find the linearization at x = a. f(x) = 3x², a = 1 (Use symbolic notation and fractions where…

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Q: ƒ(X) e F[X] be a non-constant polynomial of degree d. Prove that f(a) has degree at least over F.

A: ANSWER :

Q: - Let Q(x) be a polynomial of degree less than N. Prove that Q(x)PN(x)dx = 0.

A: Note, that this result is a specific case of orthogonality of Legendre’ s polynomials. We will prove…

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A:

Q: Find the Taylor polynomial P4(x) centered at x = 0 for the function f(x) = x – 4 cos(x). a) 0-4-x+x*…

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Q: Let P(x) be the Lagrange interpolating polynomial of f(x) = 2x2 +3 at the points xo = 0; x1 = 1 and…

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Q: 2#Find the the Taylor's polynomial P2(x)for the function f(x)=4x²e-2x about Xo-and hence find…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Determine the value of a so that x²+ax +5 f (x) = has an oblique x+1 asymptote at y = x – 4| -

A: GIven f(x)=x2+ax+5x+1 has an oblique asymptote at y= x-4we have to find the value of "a".

Q: on the closed interval Co,14], (0,14)such that f'ccF FC14D-FCO) 14-0

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Q: Show that the Maclaurin polynomials for f (x) = sin x are x2n+1 T2n+1 (x) = T2n+2 (x) = x – 3!…

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Q: Find the Taylor polynomial T3(x) for the function f centered at the number a f(x)=(ln(2x))/(3x),…

A:

Q: Find the third degree Taylor polynomial T3 (x)centered at a O T3 (x) = 3 - 6x + 9x² - 12x³ O T3…

A:

Q: Find the degree 3 Taylor polynomial T3(x) of function f(x)=(−7x+22)4/3 at a=2 T3(x)=

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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: express the quotient  P(x)/D(x)  in the form  P(x) D(x) = Q(x) +  R(x) D(x). P(x) = 8x2 − 3x − 17,…

A:

Q: Let g (x, y) = 9 sin(xy) – 11x² In(y) + 4. Find the degree 2 polynomial, p, which best approximates…

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