Second order Taylor polynomial
at x=7
Question Suppose you are estimating V7 using the second Taylor polynomial of the function Væ about...
Complete all, especially part c and d
(a) Glive the second-order Taylor polynomial T2 ( for the function () about a 16. 4+((X-16)/8)-(1/512) (X-16M2 b) Use Taylor's Theorem to give the Error Term E2(-f()T2) as a function of z and some z between 16 and az (((3/8) Z(-5/2)) (X-16) 3)/6 c) Estimate the domain of values z for which the error E2 () is less than 0.01. Enter a value p for which E2 ()I 0.01 for all 16 16+p,...
Question 1 (20 Points) Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about Xo = 0. Using 4-digit rounding arithmatic. (a). Use P2(0.7) to approximate f(0.7). (b). Find the actual error. (c). Find a bound for the error f(x) - P2(x) in using P2(x) to approximate f(x) on the interval [0, 1].
Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about xo = 0. Using 4-digit rounding arithmatic. (a). Use P2(0.7) to approximate f(0.7). (b). Find the actual error. (c). Find a bound for the error |f(x) – P2(x) in using P2(x) to approximate f(x) on the interval [0, 1].
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...
3. Suppose we approximate x H> exp(x) with its 3rd Taylor polynomial about 0. For nonnegative x, what is the greatest value of r for which Taylor's theorem guarantees this approximation has a relative error of at most 1/24?
3. Suppose we approximate x H> exp(x) with its 3rd Taylor polynomial about 0. For nonnegative x, what is the greatest value of r for which Taylor's theorem guarantees this approximation has a relative error of at most 1/24?
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.
Compute the Taylor polynomial indicated f(x)-V1 a 8 3888 Use the error bound to find the maximum possible size of the error. (Round your answer to five decimal places.) lva02-ncs.oz기 s-x 10-12 T3(8.02) S
Compute the Taylor polynomial indicated f(x)-V1 a 8 3888 Use the error bound to find the maximum possible size of the error. (Round your answer to five decimal places.) lva02-ncs.oz기 s-x 10-12 T3(8.02) S
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
8 pts . Answer parts a through e using the function f(x)- isd br cipah Tperpebynomia.ced0 Find the eighth degree Taylor polynomial, centered at 0, to approximate f(x) a. . Be sure to simplify your answer. b. Using your eighth degree polynomial from part a and Taylor's Inequality, ii fork-als,the E find the magnitude of the maximum possible error on [0, .1]. x-ato (n 1)! c. Approximateusing your eighth degree Taylor polynomial. What is the actual 1.1 error? Is it...