Given the function g(x) – 5(x – 7)*(x + 1)°(x – 4), its roots are and their multipicities are

Q: Let g (x, y) = 7 sin(xy) – 9x? In(y) + 4. Find the degree 2 polynomial, p, which best approximates g…

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Q: Find the second-degree Taylor polynomial T2(x) for the function f(x)=15+x2  at the number x=1.

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Q: The polynomial of degree 33, P(x)P(x), has a root of multiplicity 22 at x=3x=3 and a root of…

A: Given that the polynomial P (x) of degree 33, with x= 3 and x=-4 are root of multiplicity 22 and 11…

Q: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 2 and a root of multiplicity 1…

A: Given,            The polynomial of degree 3, P(x) has a root of multiplicity 2 at x=2 and a root of…

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

A: As per the question we have to find the bset fit polynomial in p2 ∈ P , to to the curve g(x)=sin(x)…

Q: on 15 e quadratic approximation of the function f (x) =5x³– 4x+ 12 at x=1 is: P 15x2 – 19x+ 17 P…

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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…

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Q: If f(x) = /4² + bx – Vcx² – dæ has a horizon- tal asymptote at y = 2 for all x b+c+d. - Vcx2 - dx…

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Q: Find the horizontal asymptote(s) of the following if there are any. x3+2 y6-y2+7 1. f(x) = 2. h(y) =…

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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…

A: Given function is f(x)=e^2x

Q: EXERCISE 4. Evaluate the following using Rationalization Method. Show your solution. Vx² + 7 – 3 lim…

A: Given  The limits are 1.  limx→3x2+7-3x+32.  limx→0x+1-1x

Q: Find the degree 3 Taylor polynomial T3(x) of function f(x) = ( – 5x + 276)7 4. - at a T3(x)

A: We need to find 3 degree Taylor Polynomial of the function f(x)=(276−5x)54 at a=4 so using Taylor…

Q: 1 Consider the function defined by f(x) over [-1, 1]. SET-UP the Lagrange 1+ 12x2 polynomial…

A: Lagrange's Interpolation formula can be defined as:…

Q: 3. Suppose the function f (x) is approximated near x= 0 by a third-degree Taylor polynomial…

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Q: The polynomial of degree 33, P(x)P(x), has a root of multiplicity 22 at x=3x=3 and a root of…

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Q: V. Provide up to the 5th degree Taylor Polynomial of the given function: f(x)= xex by about x=-1

A: Given :fx=xe-xx=-1

Q: For the given points X, = 1, x =1.5, x, = 2.5 and x, = 3. Find Lagrange Interpolation polynomial for…

A: Given function is f(x)=x2esinx+ln(sinx) Find 'f(x)' corresponding to given values of 'x' x 1 1.5…

Q: The polynomial of degree 33, P(x)P(x), has a root of multiplicity 22 at x=5x=5 and a root of…

A: Given the degree of polynomial is 3

Q: 2. For the given functions f (x), let.x, = 1,x, = 1.25, and.x, = 1.6. Construct interpolation…

A: Step:- 1 Lagrange Interpolating polynomial:- P(x)=f0 L0(x) +f1 L1(x)+ f2 L3(x)+....fn Ln(x),Here,…

Q: 2. Find the Taylor Polynomial T3(x) for the function f(x) = x-2 at a = 1.

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Q: 3/2 Construct the fourth degree Taylor polynomial at x= 0 for the function f(x) = 3(1 - x)2. P4(x) =

A: Solved below

Q: Find the fourth degree Taylor polynomial, T4(x), for f(x) at 4. f(x) = 5 In(x - 3)- 4 a) Find the…

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Q: g(x) = sinh x2

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Q: Consider a quadrature of the form 1 |æ|f(x)dx = ÷(f(-1) + 2f(0) + f(1)), (f(-1)+2f(0) + f(1)), show…

A: Solution: The objective is show that the given quadrature is exact for any polynomial f(x) of degree…

Q: 2 Find the limit infimum and supremum of 2 XA = √√√ 1+n² √1tn 2A-5 write the complete solution.

A: Limit infimum and limit suprimum

Q: 2. Find the MacLaurin polynomial of degree 16 for the function F(x)= So sin (6xt²) dt.

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Q: Find Taylor polynomials of degree 4 at 0 for the functions defined as follows.

A: Find the derivative and the values for derivatives for f(x) at point a = 0.…

Q: find the absolute maxima and minima of the func-tions on the given domains. ƒ(x, y) = x2 + y2 on the…

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Q: The Maclaurin polynomial of degree 4 for the function f(x) = cos(x) is %3D

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Q: Within the interval 2 0 has a minimum value of and a maximum value of 3.

A: Find the values of a and b

Q: |The function f(x) is approximated near x = 0 by the second degree Taylor polynomial P2(x) = 1- 7x +…

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Q: Find the asymptotes of the func 1 y = f(x) = x sin–

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Q: For the cubic polynomial function ?(?)=??3+??2+??+?,f(x)=ax3+bx2+cx+d, find ?,a, ?,b, ?,c, and ?d so…

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Q: Find the vertical and horizontal asymptote(s) of f(x).

A: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a…

Q: Find the polynomial f(x) of degree 6, 1/x which satisfies lim{1+ f(x)] =e? x3 X-0 and has local…

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Q: the polynomial of degree 4, p(x) has leading coefficient 1 had a zero of multiplicity 2 at x=2, a…

A: We are given that the polynomial p(x) has a zero of multiplicity 2 at x=2, i.e.; the polynomial has…

Q: Use Dirichlet's principle with n = 10 to find a rational approximation of T.

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Q: 1)Find the fourth degree Maclaurin polynomial for the function. f (x) = e3z

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Q: The function f(x) = cos(3x) is interpolated on the interval [О, 1/5] with a polynomial of order 3…

A: According to the given information, Consider the given function.

Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 3. y=f(x) 1…

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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: Suppose the graph of y = f(x) is given below. We happen to know that f has derivatives of all orders…

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Q: For the given points Xo = 1, x =1.5, x, = 2.5 and x3 = 3. Find Lagrange Interpolation polynomial for…

A: Given: The function is  f(x)=x2esin x+ln(sin x) The points are x0=1, x1=1.5, x2=2.5, x3=3   To…

Q: 1. For the function f(x) = /1+x, let ro = 0, x1 = 0.6, and r2 = 0.9. Con- struct Lagrange…

A: Given:

Q: Find the interpolating polynomial of the following point and function using the Lagrange…

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Q: The 2nd degree polynomial that interpolates to f(x) = cosx + sinx at x = 0, x= π/2 and x = π is best…

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Q: Find the degree 3 Taylor polynomial T;(x) of function f(x) = ( – 5x + 57) at a = 6. %3D T3(x) =

A: Function given is - f(x)=(-5x+57)4/3 We need to find Taylor polynomial T3(x) at a=6 Taylor series…

Q: The polynomial of degree 33, P(x)P(x), has a root of multiplicity 22 at x=2x=2 and a root of…

A: To find the formula of polynomial. Given the roots of P(x) with the multiplicity of the roots and…