(i) Construct the minimax polynomial p2 E P2 on the interval (-1,1] for the function g defined by g(x) = sin a.

Q: 3) Compute the Maclaurin polynomial of degree 4 for the function f(x)=cos(x) In(1-x) for -1<x<l.

A: Consider the given function f(x)=cosxln1-x   ; -1&lt;x&lt;1 The formula to find Maclaurin series,…

Q: 4. Let f(x)= a(7-a2) for all a 0 (a) Find, in terms of a, the equations of the lines tangent to…

A: Given.

Q: Given f(x) = - 3x ^ 3 - 2x - 4 verify that f(x) is invertible and, if so, find the equation of the…

A:

Q: 2. Let f(x) = 2e# – 3x² /a, whose graph is given to the right. Sketch in the tangent lines to f(x)…

A: PArt A: tangent line at x=1   The derivate of the tangent line at x=1, Find the derivative of the…

Q: The range of F in F(x) = 2 sin x; - < x< 2 T is: %3D -2SF(x)SO F(x)S2 ) -2SF(x)S2 O O

A: Given:- F(x)=2 sinx  ,-π/2 &lt;x &lt;2π To find:- Range of F(x)

Q: Determine the first and second degree Maclaurin polynomial approximations, L(x, y) and Q(x, y), for…

A: f(x,y) = xx+y + xcosxyTo find: L(x,y)  = first degree Maclaurin approximationQ(x,y) = 2nd degree…

Q: Find the the Taylor's polynomial P2(x)for the function f(x) = 5x2e-2 about xo = hence find f(0.5).…

A: Given, f(x) =5x2e-2xThe Taylor's polynomial P2(x) about x…

Q: Let f(x) = (x2 + 3x)e .Find the value of c that satisfies the conclusion of Rolle's Theorem for f on…

A:

Q: For which x value does f (x) = x - 3x2 + 1have a local maximum. CO C-1 C 1 C -2 C 2

A: Given: The function fx=x3-3x2+1, To find: point of Local maximum

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

A: The given question has been solved in step 2.

Q: b) Let f(x) = e"cos 3x, No 0, x = 0.3,1 =0.6, n = 2 %3D Construct the second Lagrange polynomial for…

A: We have fx=e2xcos3x Now,  x0=0x1=0.3x2=0.6 Therefore,  fx0=e20cos30=1fx1=e20.3cos30.3=…

Q: Let F(x) = e -5¢4 dt. Find the MacLaurin polynomial of degree 5 for F(x). Use this polynomial to…

A:

Q: Find T3 (x) (the Taylor polynomial of degree 3) for the function f at the number c. (a) f(x) 1 c= 2…

A:

Q: Find the residue of the function f(z) = 1- e2z at its pole. z4 |

A: The given problem is to find the residue of given complex variable function at its pole, we can use…

Q: 2. Find the linearization L(x) of f(x) = x³ - 2x + 3 at x = 2 and use it to approximate f(1.9) and…

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…

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

Q: 8. Consider the function f(x)=/25-x² . a. Find the linearization L(x) of f(x) at x=3.

A: Given expression is , fx=25-x2 to find out the linearization L(x) of f(x) at x=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: 1. Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: see 2nd step

Q: IB) Find the cnber of curvatee, eguation of the curde of cuuunfure f (x)> Jax of the gmph. of at x=…

A: Consider the given curve as, fx=2x at, x=4 Let y=fx=2x

Q: 6) = sin(x + # ) on [0. 0. 4 4

A:

Q: Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) = 11 tan-1(x), a…

A: The function is givne by,

Q: Find the Taylor Polynomial de degree 3 centered at a = f(x) = x ex 0³ T₂ (2) - 1 - 2 + 1 - 2 ○ T3 a)…

A:

Q: 4. For the given function f(x) = /2 + x², let xo = 0, x1 = 0.5, and x2 = 0.8. Construct a Lagrange…

A:

Q: 2. Find the constant a such that the function is continuous on the entire real number line x2- a2 w…

A: If it is continuous at x=a , then left and right limit must be same at x=a

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

A:

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

A: Given: To find Taylor polynomial T3(x) for the function f(x)=cos(x) centered at the number a=π2

Q: Find the absolute maxima and minima of the function on the given domain. f(x_ v) = 2x + 5y on the…

A: Given function f(x,y)=2x+5ywe need to find criical pointconsider f'(x)=0                     and…

Q: Find the absolute maximum and absolute minimum of f(z) = +z - 48z over the interval (4, 8).

A: We have to find the absolute maximum and absolute minimum for the function f(x)=x33+x2-48x over the…

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

A:

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

A:

Q: a) Develop a table of f(x)= e¯* + 5x for x = 2, 4, 5 and 8. b) Estimate f(3.2) using the…

A:

Q: Let f(x) = e* for 0 < x<1 a. Approximate f(0.25) using linear interpolation with xo = 0 and x1 = 0.…

A:

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: d. Find the linear approximation L(x) for f(x)=x²-x-1 at a = 1.

A: Given function is fx=x3−x−1. d We have to find the linear approximation Lx for function fx at a=1.…

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

A:

Q: 9. 3x2 Let g(x) = -2x2 r<0 (b) Prove that q is not differentiable at 0.

A:

Q: a) Express the polynomial f(x) in terms of Legendre polynomials where f(x) = 1-3x + 3x² e-2t sinh t…

A: According to our guidelines we can answer only one question and rest can be reposted.

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

A: we have to show that  Maclaurin polynomials for    f(x)=sinx  are…

Q: 1. Determine the discrete least squares trigonometric polynomial S2 (x) on the interval [-T, T] for…

A:

Q: Find the upper bound for the absolute error on the interval [xo, x4] for the Hermit polynomial…

A: Given:- f(x)=cos x x0=1 , x1=1.1

Q: Let T3 be the Maclaurin polynomial of f (x) = ex . Use the error bound to find the maximum possible…

A:

Q: 2. Find the principal part with respect to x for x 0 of the infinitesimal f(x) = = Vx + Vx. (That…

A: We have to use expansion of the function after some manipulations.

Q: If f is a quadratic function such that f(0) = 9 and f(x) x2(x + 1)3 dx is a ratianal.functian,,find…

A: This question is about finding f'(x)  at x=0  where f(x) is a rational function

Q: (a) The nth Maclaurin polynomial pn(x) -x* of a (n times differen- k! %3D k=0 tiable) function f(x)…

A: A Maclaurin polynomial (Taylor polynomial at 0) expansion is given by,