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35) Consider the series . How large do we need to choose n so that the remainder n=0 n/3 a) R, s.001 b) R, S.0001 35) Consider the series . How large do we need to choose n so that the remainder...
A) 0.2028 B) 0.4055 C) 0.47 D) 0.235 For the series given, determine how large n must be so that ...
please
A) 0.2028 B) 0.4055 C) 0.47 D) 0.235 For the series given, determine how large n must be so that using the nth partial sum to approximate the series gives an error of no more than the stated error. 20) 20) A) 600 B) 1500 C) 300 D) 3000 Use the Comparison Test to determine if the series converges or diverges. an=_cosn -4 t cos n n-1 n A) diverges S>소 Converge 6)or verges 21) due-toe-sones, 21) n s...
A tinctlon of series y I Taylor The 6. Taylor's Remainder Theorem. fn)(0) where fw) is the n-th d...
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...
(a) Find the approximation Sio for J sin zdr and the corresponding error Es (b) How large do we h...
(a) Find the approximation Sio for J sin zdr and the corresponding error Es (b) How large do we have to choose n so that the approximation Sn is accurate within 0.00001.
(a) Find the approximation Sio for J sin zdr and the corresponding error Es (b) How large do we have to choose n so that the approximation Sn is accurate within 0.00001.
Problem 3. Consider the series: 1 n [ln (n)]4 n=2 a) (6 pts) Use the integral...
Problem 3. Consider the series: 1 n [ln (n)]4 n=2 a) (6 pts) Use the integral test to show that the above series is convergent. b) (4 pts) How many terms do we need to add to approximate the sum within Error < 0.0004.
B) Consider the series reaction A R S that we studied in lecture, where both reactions...
B) Consider the series reaction A R S that we studied in lecture, where both reactions are first order and irreversible. A batch reactor is loaded with Cao=4 mol/L and k1=0.25 min!. Plot CA, CR, and Cs as a function of time for a set of different ka's ranging from 0.025 to 2.5 min!. Comment on the dynamics that you observe for the different cases. Which rate constants and operating conditions are optimal if your goal is to maximize the...
b)first look at the equation attached generalise the equation in case of very large n(n>>р.link this equation to circulton motion of electron so induce r n is propotional to nA2> (N+ p)...
b)first look at the equation attached generalise the equation in case of very large n(n>>р.link this equation to circulton motion of electron so induce r n is propotional to nA2> (N+ p) Planck constant) R . Rydberg constant (hR-136 eV, series), 2(Balmer), 3(Paschen), 4Brackett), 5(Pfund)
b)first look at the equation attached generalise the equation in case of very large n(n>>р.link this equation to circulton motion of electron so induce r n is propotional to nA2> (N+ p) Planck constant) R...
1. (a) We need to calculate accurate values of the function for very large values of x. However, it is found that ju...
1. (a) We need to calculate accurate values of the function for very large values of x. However, it is found that just programming this formula into a computer gives very poor accuracy for large x Explain why this happens, and show how to re-write the function so that it can be used reliably, even when x is large. [6 points] (b) In diffraction theory, it is sometimes necessary to evaluate the function sin θ f(x) for small to moderate...
6. We want to use the Integral Test to show that the positive series a converges....
6. We want to use the Integral Test to show that the positive series a converges. All of the following need to be done except one. Which is the one we don't need to do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = a, for all n. (b) Show that ſ f(z) dr converges. (e) Show that lim Ss6 f(x) dx exists. (d) Show that lim sexists. 7. Suppose...
(5 pts) Consider the function f(x) = 8e7r. We want to find the Taylor series of...
(5 pts) Consider the function f(x) = 8e7r. We want to find the Taylor series of f(x) at x = x = -5. (a) The nth derivative of f(x)is f(n)(x) = 8(7)^ne^(7x) At = -5, we get f(n)(-5) = 8(7)^ne^-35 (c) The Taylor series at x = -5 is too T(x) = (3/7^n](^-35)n!/(n+ (x + 5)” n=0 (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+oo 1/(x+1) |x + 51 an and so...
(5 pts) Consider the function f(x) = 8e7x. We want to find the Taylor series of...
(5 pts) Consider the function f(x) = 8e7x. We want to find the Taylor series of f(x) at x = -5. (a) The nth derivative of f(x) is f(n)(x) = At r = -5, we get f(n)(-5) = (c) The Taylor series at r = -5 is +00 T(x) = { (3+5)" n=0 = (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+too an and so its radius of convergence is R= |x...
please
A) 0.2028 B) 0.4055 C) 0.47 D) 0.235 For the series given, determine how large n must be so that using the nth partial sum to approximate the series gives an error of no more than the stated error. 20) 20) A) 600 B) 1500 C) 300 D) 3000 Use the Comparison Test to determine if the series converges or diverges. an=_cosn -4 t cos n n-1 n A) diverges S>소 Converge 6)or verges 21) due-toe-sones, 21) n s...
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...
(a) Find the approximation Sio for J sin zdr and the corresponding error Es (b) How large do we have to choose n so that the approximation Sn is accurate within 0.00001.
(a) Find the approximation Sio for J sin zdr and the corresponding error Es (b) How large do we have to choose n so that the approximation Sn is accurate within 0.00001.
Problem 3. Consider the series: 1 n [ln (n)]4 n=2 a) (6 pts) Use the integral test to show that the above series is convergent. b) (4 pts) How many terms do we need to add to approximate the sum within Error < 0.0004.
B) Consider the series reaction A R S that we studied in lecture, where both reactions are first order and irreversible. A batch reactor is loaded with Cao=4 mol/L and k1=0.25 min!. Plot CA, CR, and Cs as a function of time for a set of different ka's ranging from 0.025 to 2.5 min!. Comment on the dynamics that you observe for the different cases. Which rate constants and operating conditions are optimal if your goal is to maximize the...
b)first look at the equation attached generalise the equation in case of very large n(n>>р.link this equation to circulton motion of electron so induce r n is propotional to nA2> (N+ p) Planck constant) R . Rydberg constant (hR-136 eV, series), 2(Balmer), 3(Paschen), 4Brackett), 5(Pfund)
b)first look at the equation attached generalise the equation in case of very large n(n>>р.link this equation to circulton motion of electron so induce r n is propotional to nA2> (N+ p) Planck constant) R...
1. (a) We need to calculate accurate values of the function for very large values of x. However, it is found that just programming this formula into a computer gives very poor accuracy for large x Explain why this happens, and show how to re-write the function so that it can be used reliably, even when x is large. [6 points] (b) In diffraction theory, it is sometimes necessary to evaluate the function sin θ f(x) for small to moderate...
6. We want to use the Integral Test to show that the positive series a converges. All of the following need to be done except one. Which is the one we don't need to do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = a, for all n. (b) Show that ſ f(z) dr converges. (e) Show that lim Ss6 f(x) dx exists. (d) Show that lim sexists. 7. Suppose...
(5 pts) Consider the function f(x) = 8e7r. We want to find the Taylor series of f(x) at x = x = -5. (a) The nth derivative of f(x)is f(n)(x) = 8(7)^ne^(7x) At = -5, we get f(n)(-5) = 8(7)^ne^-35 (c) The Taylor series at x = -5 is too T(x) = (3/7^n](^-35)n!/(n+ (x + 5)” n=0 (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+oo 1/(x+1) |x + 51 an and so...
(5 pts) Consider the function f(x) = 8e7x. We want to find the Taylor series of f(x) at x = -5. (a) The nth derivative of f(x) is f(n)(x) = At r = -5, we get f(n)(-5) = (c) The Taylor series at r = -5 is +00 T(x) = { (3+5)" n=0 = (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+too an and so its radius of convergence is R= |x...
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