10) Consider the function f(x) = √/X² Let T be the n Find T, and T₂ an T₂ is |R₂| ≤ 1th degree Taylor approx of f(1.02) about x=| over/under estimate of 1.02
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- Find the Taylor polynomials p1, ..., p5 centered at a=0 for f(x)=9e^−x.1. Find the Taylor polynomial T2(?) for the function f(x) = 2e^(2x) at x =0. 2. Let T3 be the Maclaurin polynomial of f(x) = e^x. Use the Error Bound to find the maximum possible value of |f(1.6)−T3(1.6)|. (Use decimal notation. Give your answer to four decimal places.)Let f(x) 3(x+1)(x-:)x- 1). Use the Bisection method on tle (-2, 1.5] b. -1.25, 2.5] a. 3. Use the Bisection method to find solutions accurate to within 10-2 for x'-7x+14x-6 =0 on each interval. [0, 1] b. [1,3.2] [3.2, 4] a. C. '-2r-4.+ 4x +4 0 Use the Biseetion method to find solutions accurate to within 10 forx on each interval. 4. d. |-1,0| 2.
- Let f(x) = e^x. Find the polynomial P2(x) of degree at most 2 such thatP2(1) = f(1), P2(2) = f(2), P2(3) = f(3) by using a divided-difference table. (Donot use decimal approximations for the number e.)calculate M6 for f(x)=7(In(x^2)) over [1,2]Let f(x) = e^xFind the polynomial H3(x) of degree at most 3 such thatH3(1) = f(1), H3(2) = f(2), H3'(1) = f'(1), H3'(2) = f'(2) by using a (generalized)divided-difference table. (Do not use decimal approximations for the number e.)
- "Let T_2(x) be the Taylor polynomial of f(x)=\sqrt(x) centered at a=4. Apply the Error Bound to find the maximum value of the error if we approximate \sqrt(x) with T_2(x) for x in [3.9,4]."8.Expand the function F(x) =e ^3x-1 by using the Taylor order 4 polynomial, then approximate the value of the function at the point x -1 and calculate the error!Suppose g is a function which has continuous derivatives, and that g(8) = -2, g(8) = 3. g"(8) = -4, g"(8) = 4. %3D (a) What is the Taylor polynomial of degree 2 for g near 8? P:(z) = (b) What is the Taylor polynomial of degree 3 for g near 8? Pa(z) = (c) Use the two polynomials that you found in parts (a) and (b) to approximate g(8.1). With Pa, g(8.1) = With Ps, g(8.1) =
- Consider the following function. f(x)=x^(-5), a=1, n=2, 0.8<=x<=1.2 Approximate f by a Taylor polynomial with degree n at the number a. T2(x)=consider the ff. function: f(x, y) = cot" ^ (1+x) - 2 ex + ³y If x = √5² ++²₂² and y = 3t + tan (1-5), use the multivariate chain wie to evaluate of when 5=1 and + = -1- as6. Use the Mean Value Theorem to find all values of c in (6, 14) such that ƒ'(c) = f(b)-f(a) b-a for f(x)=√√√2x - 3 on the interval [6, 14]