3. Approximate the function f(x) = Vx by T4(x), the Taylor polynomial of degree 4 centred...
2. (a) (4 points) Find the Taylor polynomial T3(x) for the function f(z) = zez about a = 1, Please, do NOT use notation, you have to write all terms of Ts and they have to be simplified. b) (4 points) Use the Taylor's inequality to estimate the accuracy of the approximation f(x)T3(x) for くバ, (Do NOT give decimal fractions as your answer, Do NOT use a calculator leave your answer as an algebraic expression.) 2. (a) (4 points) Find...
(2) Consider the following function: (a) Using a Taylor polynomial of degree three (i.e. up to the term z3, included) and centred at Zo = 1, evaluate V2 correct to the fifth significant digit. (b) Compare your result using Taylor's formula with the "true" numerical value v2 1.41421, accurate to the fifth significant digit. What is the value of the remainder R4 for the Taylor formula used in (a)? (c) How does the approximation used in (a) improve if we...
Consider the following function. (t) = 4/7,6 1,0 3,0.9 5511 (a) Approximate by a Taylor polynomial with degreen at the number a T5(X) - + + 313 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) when x lies in the given interval. (Round the answer to eight decimal places.) IR 150.00105548 X
question b please Consider the following function f(x) -x6/7, a-1, n-3, 0.7 sx 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a 343 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ,(x) when x lies in the given interval. (Round your answer to eight decimal places.) IR3(x)0.00031049 (c) Check your result in part (b) by graphing Rn(x)l 2 1.3 0.00015 0 0.9 1.0 11 -0.00005 0.00010 -0.00010 0.00005 0.00015 0.8...
(1 point) Consider a function f(x) that has a Taylor Series centred at x = -3 given by an(x + 3)" n=0 If the radius of convergence for this Taylor series is R = 4, then what can we say about the radius of convergence of the Power Series Š an -(x + 3)" ? no n=0 A. R= 2 4 OB.R = 6 OC. R = 4 OD. R = 24 O E. R= 8 F. It is impossible...
A function f, which has derivatives for all orders for all real numbers, has a 3rd degree Taylor polynomial for f centered at x = 5. The 4th derivative of f satisfies the inequality f^(4)(x) ≤ 6 for all x the interval from 4.5 to 5 inclusive. Find the LaGrange error bound if the 3rd degree Taylor polynomial is used to estimate f(4.5). You must show your work but do not need to evaluate the remainder expression.
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between Tn (x) and TR+1()? (c) You might want to approximate cos(az) for all in 0 xS /2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a -2, i.e. f(x)...
point) Consider a function f(x) that has a Taylor Series centred at x = 5 given by ſan(x – 5)" n=0 he radius of convergence for this Taylor series is R= 4, then what can we say about the radius of convergence of the Power Series an ( 5)"? nons A. R= 20 B.R= 8 C. R=4 D. R= E. R= 2 F. It is impossible to know what R is given this information. point) Consider the function f(x) =...
(1 point) Consider a function f(x) that has a Taylor Series centred at z = 1 given by 00 Ż an(z - 1)" D If the radius of convergence for this Taylor series is R-4, then what can we say about the radius of convergence of the Power Series (x - 1)"? 0720 O AR 6 B. R=24 OC. R-2 OD. R = 8 O ER=4 OF. It is impossible to know what R is given this information
(1 point) Determine the Taylor Series of the function 825 f(3) = (1 - x)? centred at 3 = 0. A. 82n +5 B. C. 8n24 8 D. +6 0 12 +1 (-8)",5m