2. sin(0.2),f(x)= sin x
Theorem 10.1: The Lagrange Error Bound for Pn(a) Suppose f and all its derivatives are continuous. If P,() is the nth Taylor polynomial for f(a) about a, then n-+1 where f(n+) M on the interval between a and a.
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In Exercises 1-8, use Theorem 10.1 to find a bound for the error in approximating the quantity wi...
5) a) Use the alternating estimation theorem to give the maximum error for approximating sin 3 us...
5) a) Use the alternating estimation theorem to give the maximum error for approximating sin 3 using a third degree Maclaurin polynomial for sin a. b) Use Taylor's inequality to estimate the accuracy of a fourth degree Taylor polynomial for sin a centered atfor 0 s a s
5) a) Use the alternating estimation theorem to give the maximum error for approximating sin 3 using a third degree Maclaurin polynomial for sin a. b) Use Taylor's inequality to estimate the...
Extra Credit Problem a. Find a bound on the error incurred in approximating fx- Inx by the fourth...
Extra Credit Problem a. Find a bound on the error incurred in approximating fx- Inx by the fourth Taylor polynomial of fat x-1 in the interval l1, 1.51. b. Approximate the area under the graph of f fromx-1 tox-15 by using the fourth Taylor polynomial found in part a. c. What is the actual error? (Hint: use integration by parts to evaluate the definite integral of fin the intervab.
Extra Credit Problem a. Find a bound on the error incurred...
Please do questions 21, 25, 29, and 33. Thanks! In Exercises 21 - 24, approximate the...
Please do questions 21, 25, 29, and 33.
Thanks!
In Exercises 21 - 24, approximate the function value with the indicated Taylor polynomial and give approximate bounds on the error. 21. Approximate sin 0.1 with the Maclaurin polynomial of de- gree 3. Exercises 25 - 28 ask for an n to be found such that pn(x) ap- proximates f(x) within a certain bound of accuracy. 25. Find n such that the Maclaurin polynomial of degree n of f(x) = et...
Let f be a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above.
Let f be a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above. (a) Write the second-degree Taylor polynomial for f about x = 0 and use it to approximate f(0.2). (b) Let g be a function such that g(x) =f(x3). Write the fifth-degree Taylor polynomial for g', the derivative of g, about x = 0. (c) Write the third-degree Taylor polynomial for f about x =...
I don't understand how to find the bounds on the error for number 21 and 23
I don't understand how to find the bounds on the error for
number 21 and 23
20, f(x) = x2 cos x, n = 2, c = π and a In Exercises 21-24, approximate the function value with the indicated Taylor polynomial and give approximate bounds on the error. etter 21. Approximate sin 0.1 with the Maclaurin polynomial of de- gree 3. gree 22. Approximate cos 1 with the Maclaurin polynomial of de- gree 4. gree 23. Approximate v10 with...
Week 2: Problem 14 Previous Problem Problem List Next Problenm 1 point) Use the Error Bound to find the least possible value of N for which Error(Sy) S 1 x 10-9 in approximating using the result...
Week 2: Problem 14 Previous Problem Problem List Next Problenm 1 point) Use the Error Bound to find the least possible value of N for which Error(Sy) S 1 x 10-9 in approximating using the result that Ka(b-a)s Error SN) S 180N4 where K4 is the least upper bound for all absolute values of the fourth derivatives of the function 2e on the interval [a,b].
Week 2: Problem 14 Previous Problem Problem List Next Problenm 1 point) Use the Error...
2. a) Find Ts(x), the third degree Taylor polynomial about x -0, for the function e2 b) Find a bound for the error in the interval [0, 1/2] 3. The following data is If all third order differences (not...
2. a) Find Ts(x), the third degree Taylor polynomial about x -0, for the function e2 b) Find a bound for the error in the interval [0, 1/2] 3. The following data is If all third order differences (not divided differences) are 2, determine the coefficient of x in P(x). prepared for a polynomial P of unknown degree P(x) 2 1 4 I need help with both. Thank you.
Problem 1 (hand-calculation): Given f(!)-ze" for z є о.05], apply Taylor's theorem using 10-0 in ...
Problem 1 (hand-calculation): Given f(!)-ze" for z є о.05], apply Taylor's theorem using 10-0 in the following exercises. (a) Construct the Taylor polynomials of degree 4, p(x) (b) Estimate the error associated with the polynomial in part (a) by computing an upper bound of the absolute value of the remainder
Problem 1 (hand-calculation): Given f(!)-ze" for z є о.05], apply Taylor's theorem using 10-0 in the following exercises. (a) Construct the Taylor polynomials of degree 4, p(x) (b) Estimate the...
(1 point) Taylor's Remainder Theorem: Consider the function 1 f(x) = The third degree Taylor polynomial...
(1 point) Taylor's Remainder Theorem: Consider the function 1 f(x) = The third degree Taylor polynomial of f(x) centered at a = 2 is given by 1 3 12 60 P3(x) = -(x-2) + -(x - 2)2 – -(x - 2) 23 22! 263! Given that f (4)(x) = how closely does this polynomial approximate f(x) when x = 2.4. That is, if R3(x) = f(x) – P3(x), how large can |R3 (2.4) be? |R3(2.4) 360 x (1 point) Taylor's...
Compute the Taylor polynomial indicated f(x)-V1 a 8 3888 Use the error bound to find the maximum ...
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
5) a) Use the alternating estimation theorem to give the maximum error for approximating sin 3 using a third degree Maclaurin polynomial for sin a. b) Use Taylor's inequality to estimate the accuracy of a fourth degree Taylor polynomial for sin a centered atfor 0 s a s
5) a) Use the alternating estimation theorem to give the maximum error for approximating sin 3 using a third degree Maclaurin polynomial for sin a. b) Use Taylor's inequality to estimate the...
Extra Credit Problem a. Find a bound on the error incurred in approximating fx- Inx by the fourth Taylor polynomial of fat x-1 in the interval l1, 1.51. b. Approximate the area under the graph of f fromx-1 tox-15 by using the fourth Taylor polynomial found in part a. c. What is the actual error? (Hint: use integration by parts to evaluate the definite integral of fin the intervab.
Extra Credit Problem a. Find a bound on the error incurred...
Please do questions 21, 25, 29, and 33.
Thanks!
In Exercises 21 - 24, approximate the function value with the indicated Taylor polynomial and give approximate bounds on the error. 21. Approximate sin 0.1 with the Maclaurin polynomial of de- gree 3. Exercises 25 - 28 ask for an n to be found such that pn(x) ap- proximates f(x) within a certain bound of accuracy. 25. Find n such that the Maclaurin polynomial of degree n of f(x) = et...
I don't understand how to find the bounds on the error for
number 21 and 23
20, f(x) = x2 cos x, n = 2, c = π and a In Exercises 21-24, approximate the function value with the indicated Taylor polynomial and give approximate bounds on the error. etter 21. Approximate sin 0.1 with the Maclaurin polynomial of de- gree 3. gree 22. Approximate cos 1 with the Maclaurin polynomial of de- gree 4. gree 23. Approximate v10 with...
Week 2: Problem 14 Previous Problem Problem List Next Problenm 1 point) Use the Error Bound to find the least possible value of N for which Error(Sy) S 1 x 10-9 in approximating using the result that Ka(b-a)s Error SN) S 180N4 where K4 is the least upper bound for all absolute values of the fourth derivatives of the function 2e on the interval [a,b].
Week 2: Problem 14 Previous Problem Problem List Next Problenm 1 point) Use the Error...
Problem 1 (hand-calculation): Given f(!)-ze" for z є о.05], apply Taylor's theorem using 10-0 in the following exercises. (a) Construct the Taylor polynomials of degree 4, p(x) (b) Estimate the error associated with the polynomial in part (a) by computing an upper bound of the absolute value of the remainder
Problem 1 (hand-calculation): Given f(!)-ze" for z є о.05], apply Taylor's theorem using 10-0 in the following exercises. (a) Construct the Taylor polynomials of degree 4, p(x) (b) Estimate the...
(1 point) Taylor's Remainder Theorem: Consider the function 1 f(x) = The third degree Taylor polynomial of f(x) centered at a = 2 is given by 1 3 12 60 P3(x) = -(x-2) + -(x - 2)2 – -(x - 2) 23 22! 263! Given that f (4)(x) = how closely does this polynomial approximate f(x) when x = 2.4. That is, if R3(x) = f(x) – P3(x), how large can |R3 (2.4) be? |R3(2.4) 360 x (1 point) Taylor'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
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
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