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5. Determine values for N for MN, TN, and SN, so that the corresponding approximations of e dr of...
(2.5 pts) Consider a numerical approximation to s° V1 + x*dx (our methods of integrating don't work for this function, so it is our only option). For each of Ln, Rn, Mn, Tn, and Sn find n so that...
(2.5 pts) Consider a numerical approximation to s° V1 + x*dx (our methods of integrating don't work for this function, so it is our only option). For each of Ln, Rn, Mn, Tn, and Sn find n so that the approximation is accurate to six decimal places (i.e. off by no more than 10-6) Note: this problem deals strictly with finding the value of K and then choosing n so that the error is small enough. You do not need...
8. .53 points sCacET6 77.026 Find the approximations Ln, Rn, Tn, and Mn for n = 5, 10, and 20. Th...
both
8. .53 points sCacET6 77.026 Find the approximations Ln, Rn, Tn, and Mn for n = 5, 10, and 20. Then compute the corresponding errors EL, ER, ET, and EM. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) 10 20 EL ET 10 20 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, EL and ER...
Find the approximations TM, and S, for n = 6 and 12. Then compute the corresponding...
Find the approximations TM, and S, for n = 6 and 12. Then compute the corresponding actual errors Et, Em and Es. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) What observations can you make? In particular, what happens to the errors when n is doubled? 33.r'da 133 n To Mn Sn 6 12 n ET EM Es 6 12 Et and Em are decrease by a factor...
O 6.26/12.5 points | Previous Answers SCalcET8 7.7.508.XP 5 (a) Find the approximations T4 and M4...
O 6.26/12.5 points | Previous Answers SCalcET8 7.7.508.XP 5 (a) Find the approximations T4 and M4 for 15e1/x dx. (Round your answers to six decimal places.) T4= 30.478393 Ma =30.213103 (b) Estimate the errors in the approximations of part (a). (Round your answers to six decimal places.) ETI 0.177493 X |EMl S 0.087797 X (c) How large do we have to choose n so that the approximations T and M, to the integral in part (a) are accurate to within...
5. Let Mn(x) be the nth Maclaurin polynomial for f(x) e as given in the text. Use the error formula to a value of n so that |Mn (2) e10-4. You will likely want to use a calculator to determine the va...
5. Let Mn(x) be the nth Maclaurin polynomial for f(x) e as given in the text. Use the error formula to a value of n so that |Mn (2) e10-4. You will likely want to use a calculator to determine the value of n. You might want to use the fact that e2 < 8 when working with the error formula.
5. Let Mn(x) be the nth Maclaurin polynomial for f(x) e as given in the text. Use the error...
5." 9 sin(x) dx. (Round your answers to six decimal places.) (a) Find the approximations T10,...
5." 9 sin(x) dx. (Round your answers to six decimal places.) (a) Find the approximations T10, M10, and S10 for T10- M10 = S10= Find the corresponding errors ET, Em, and Es. (Round your answers to six decimal places.) ET= EM= Es= (b) Compare the actual errors in part (a) with the error estimates given by the Theorem about Error Bounds for Trapezoidal and Midpoint Rules and the Theorem about Error Bound for Simpson's Rule. (Round your answers to six...
6. (5 pts) [MATH 4620] Use a rational function r(r) for Padé approximations of f(x)= x sinx with degrees m Compare the result at xi = 0.1 i, for i n = 3 = 1,2, 3 ,4,5, with the actual values f(xi...
6. (5 pts) [MATH 4620] Use a rational function r(r) for Padé approximations of f(x)= x sinx with degrees m Compare the result at xi = 0.1 i, for i n = 3 = 1,2, 3 ,4,5, with the actual values f(xi ).
6. (5 pts) [MATH 4620] Use a rational function r(r) for Padé approximations of f(x)= x sinx with degrees m Compare the result at xi = 0.1 i, for i n = 3 = 1,2, 3 ,4,5,...
Problem 5.4 (10 points) Let (Sn)n-01. be a simple, symmetric random walk with starting value So-s e R. (a) Show that ES for alln0 b) Show that ElSn+1 Sn] Sn for 0. (c)Suppose that (Sn)n-0,12,. . deno...
Problem 5.4 (10 points) Let (Sn)n-01. be a simple, symmetric random walk with starting value So-s e R. (a) Show that ES for alln0 b) Show that ElSn+1 Sn] Sn for 0. (c)Suppose that (Sn)n-0,12,. . denotes the profit and loss from $1 bets of a gambler with initial capital So-s who is repeatedly playing a fair game with 50% chances to win or lose her stake. What are the interpretations of the results in (a) and (b)?
Problem 5.4...
Please show all work and answer 5) For each of the integrals in problems a c below, first sketch the corresponding area, and then approximate the area using the right and left endpoint approximations...
Please show all work and answer
5) For each of the integrals in problems a c below, first sketch the corresponding area, and then approximate the area using the right and left endpoint approximations and the Trapezoid Rule, all with n = 4 . From your sketch alone determine if each approximation is an overestimate, an underestimate, or if there is not enough information to tell. Finally determine the value of n for which the Simpson Rule would approximate the...
Homework problem: Singular Value Decomposition Let A E R n 2 mn. Consider the singular value...
Homework problem: Singular Value Decomposition Let A E R n 2 mn. Consider the singular value decomposition A = UEVT. Let u , un), v(1),...,v(m), and oi,... ,ar denote the columns of U, the columns of V and the non-zero entries (the singular values) of E, respectively. Show that 1. ai,.,a are the nonzero eigenvalues of AAT and ATA, v(1)... , v(m) the eigenvectors of ATA and u1)...,un) (possibly corresponding to the eigenvalue 0) are the eigenvectors of AAT are...
(2.5 pts) Consider a numerical approximation to s° V1 + x*dx (our methods of integrating don't work for this function, so it is our only option). For each of Ln, Rn, Mn, Tn, and Sn find n so that the approximation is accurate to six decimal places (i.e. off by no more than 10-6) Note: this problem deals strictly with finding the value of K and then choosing n so that the error is small enough. You do not need...
both
8. .53 points sCacET6 77.026 Find the approximations Ln, Rn, Tn, and Mn for n = 5, 10, and 20. Then compute the corresponding errors EL, ER, ET, and EM. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) 10 20 EL ET 10 20 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, EL and ER...
Find the approximations TM, and S, for n = 6 and 12. Then compute the corresponding actual errors Et, Em and Es. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) What observations can you make? In particular, what happens to the errors when n is doubled? 33.r'da 133 n To Mn Sn 6 12 n ET EM Es 6 12 Et and Em are decrease by a factor...
O 6.26/12.5 points | Previous Answers SCalcET8 7.7.508.XP 5 (a) Find the approximations T4 and M4 for 15e1/x dx. (Round your answers to six decimal places.) T4= 30.478393 Ma =30.213103 (b) Estimate the errors in the approximations of part (a). (Round your answers to six decimal places.) ETI 0.177493 X |EMl S 0.087797 X (c) How large do we have to choose n so that the approximations T and M, to the integral in part (a) are accurate to within...
5. Let Mn(x) be the nth Maclaurin polynomial for f(x) e as given in the text. Use the error formula to a value of n so that |Mn (2) e10-4. You will likely want to use a calculator to determine the value of n. You might want to use the fact that e2 < 8 when working with the error formula.
5. Let Mn(x) be the nth Maclaurin polynomial for f(x) e as given in the text. Use the error...
5." 9 sin(x) dx. (Round your answers to six decimal places.) (a) Find the approximations T10, M10, and S10 for T10- M10 = S10= Find the corresponding errors ET, Em, and Es. (Round your answers to six decimal places.) ET= EM= Es= (b) Compare the actual errors in part (a) with the error estimates given by the Theorem about Error Bounds for Trapezoidal and Midpoint Rules and the Theorem about Error Bound for Simpson's Rule. (Round your answers to six...
6. (5 pts) [MATH 4620] Use a rational function r(r) for Padé approximations of f(x)= x sinx with degrees m Compare the result at xi = 0.1 i, for i n = 3 = 1,2, 3 ,4,5, with the actual values f(xi ).
6. (5 pts) [MATH 4620] Use a rational function r(r) for Padé approximations of f(x)= x sinx with degrees m Compare the result at xi = 0.1 i, for i n = 3 = 1,2, 3 ,4,5,...
Problem 5.4 (10 points) Let (Sn)n-01. be a simple, symmetric random walk with starting value So-s e R. (a) Show that ES for alln0 b) Show that ElSn+1 Sn] Sn for 0. (c)Suppose that (Sn)n-0,12,. . denotes the profit and loss from $1 bets of a gambler with initial capital So-s who is repeatedly playing a fair game with 50% chances to win or lose her stake. What are the interpretations of the results in (a) and (b)?
Problem 5.4...
Please show all work and answer
5) For each of the integrals in problems a c below, first sketch the corresponding area, and then approximate the area using the right and left endpoint approximations and the Trapezoid Rule, all with n = 4 . From your sketch alone determine if each approximation is an overestimate, an underestimate, or if there is not enough information to tell. Finally determine the value of n for which the Simpson Rule would approximate the...
Homework problem: Singular Value Decomposition Let A E R n 2 mn. Consider the singular value decomposition A = UEVT. Let u , un), v(1),...,v(m), and oi,... ,ar denote the columns of U, the columns of V and the non-zero entries (the singular values) of E, respectively. Show that 1. ai,.,a are the nonzero eigenvalues of AAT and ATA, v(1)... , v(m) the eigenvectors of ATA and u1)...,un) (possibly corresponding to the eigenvalue 0) are the eigenvectors of AAT are...
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