(1 point) Taylor's Remainder Theorem: Consider the function 1 f(x) = The third degree Taylor polynomial...
a) Use an appropriate second degree Taylor polynomial to approximate cos(0.0002). b) Apply Taylor's Theorem to guarantee a level of accuracy for the result of Part a). c) Find a Maclaurin polynoinial suitable for approximaying cos(0.0002) with an error of less than 10-30.. You need not carry out the substitution, but you should explain how Taylor's Theorem guarantees that your pokynomail works.
a tinctlon of series y I Taylor The 6. Taylor's Remainder Theorem. fn)(0) where fw) is the n-th derivative of f, and the remainder term Ry is given by NN+1 for some point c between 0 and z. (Note. You do not need to prove Taylor's Remainder Theorem.) Problems (a) (5%) write this series for the function ez for a general N (b) (10%) Apply Taylor's Remainder Theorem to show that the Taylor series of function f = ez converges...
Find Ts(x): Taylor polynomial of degree 5 of the function f(z) -cos( at a0 Preview Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.002412 of the right answer Preview Find Ts(x): Taylor polynomial of degree 5 of the function f(z) -cos( at a0 Preview Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.002412 of the right answer Preview
Find T5(a): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = T5(x) = Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.001774 of the right answer. Assume for simplicity that we limit ourselves to a < 1. nial of degree 5 of the function f(x) = cos(x) at a = 0.
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 the function f(x) = xin(x). Let T, be the degree Taylor approximation of f(2) about x = 1. Find: T = T = Use 3 decimal places in your answer, but make sure you carry all decimals when performing calculations T3 is an (over/under) estimate of f(2). If R3 is the remainder given by the Lagrange Remainder Formula: |R3|
(1 point) Find the degree 3 Taylor polynomial T3(x) centered at a = 4 of the function f(x) = (-5x + 24)312]. T3(x) = ? ✓ The function f(x) = (-5x + 24)32) equals its third degree Taylor polynomial T3 (x)/centered at a = 4l. Hint: Graph both of them. If it looks like they are equal, then do the algebra.
(1 point) Find the polynomial of degree 9 (centered at zero) that best approximates f(x) = ln(° +5). Hint: First find a Taylor polynomial for g(x) = ln(x + 5), then use this to find the Taylor polynomial you want 1/2 Now use this polynomial to approximate L'iniz? +5) da. -1/2 Lis(z) dx =
(1 point) Find the polynomial of degree 9 (centered at zero) that best approximates f(x) 71 +23 Hint: First find a Taylor polynomial for g(2) vite then use this to find the Taylor polynomial you want. 1/2 Now use this polynomial to approximate 1 dx. 1+ 3 Do" s(2) de
16. (a) Approximate f(r)= xlnx by a Taylor polynomial with degree 3 at a=1. (b) Estimate the accuracy of the approximation f (x) T (x) when x lies in the interval 0.5 rs 1.5 17. Find the first three nonzero terms in the Maclaurin series for the function f (x) = --_" and (r+3) its radius of convergence. 16. (a) Approximate f(r)= xlnx by a Taylor polynomial with degree 3 at a=1. (b) Estimate the accuracy of the approximation f...