Problem 13. (1 point) Consider a function f(x) that has a Taylor Series centred at x...
Problem 13. (1 point) Consider a function f(x) that has a Taylor Series centred at x = - 1 given by È anco an(x + 1)" no If the radius of convergence for this Taylor series is R= 8, then what can we say about the radius of convergence of the Power Series (x + 1)"? O AR= 8 5 OB. R=4 O C. R= 16 ODR = 40 O E. R=8 OF. It is impossible to know what R...
(1 point) Consider a function f(x) that has a Taylor Series centred at z = 1 given by 00 Ż an(z - 1)" D If the radius of convergence for this Taylor series is R-4, then what can we say about the radius of convergence of the Power Series (x - 1)"? 0720 O AR 6 B. R=24 OC. R-2 OD. R = 8 O ER=4 OF. It is impossible to know what R is given this information
(1 point) Consider a function f(x) that has a Taylor Series centred at x = -3 given by an(x + 3)" n=0 If the radius of convergence for this Taylor series is R = 4, then what can we say about the radius of convergence of the Power Series Š an -(x + 3)" ? no n=0 A. R= 2 4 OB.R = 6 OC. R = 4 OD. R = 24 O E. R= 8 F. It is impossible...
(1 point) Consider a function f(x) that has a Taylor Series centred at x = 1 given by Žar(2 – 1)" n0 If the radius of convergence for this Taylor series is R=2, then what can we say about the radius of convergence of the Power Series an (2 – 1)"? hins A. R= 2 5 OB. R=4 OC. R=2 OD. R=1 O ER= 10 OF. It is impossible to know what R is given this information.
(1 point) Consider a function f(x) that has a Taylor Series centred at x = 1 given by Žar(2 – 1)" n0 If the radius of convergence for this Taylor series is R=2, then what can we say about the radius of convergence of the Power Series an (2 – 1)"? hins A. R= 2 5 OB. R=4 OC. R=2 OD. R=1 O ER= 10 OF. It is impossible to know what R is given this information.
point) Consider a function f(x) that has a Taylor Series centred at x = 5 given by ſan(x – 5)" n=0 he radius of convergence for this Taylor series is R= 4, then what can we say about the radius of convergence of the Power Series an ( 5)"? nons A. R= 20 B.R= 8 C. R=4 D. R= E. R= 2 F. It is impossible to know what R is given this information. point) Consider the function f(x) =...
Find a power series representation for the function. f(x) = فيه (x – 4)2 00 f(x) = Σ no Determine the radius of convergence, R. R = Evaluate the indefinite integral as a power series. Je at c+ Σ ΦΟ η = Ο What is the radius of convergence R? R = Find the radius of convergence, R, of the series. 3n Σ n! n=1 R= Find the interval, 1, of convergence of the series. (Enter your answer using interval...
(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 answer all, be explanatory but concise. Thanks. Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. Consider the differential equation y'(t) - 4y(t)- 8, y(0)4. a. Find a power series for the solution of the differential equation b. ldentify the function represented by the power series. Use a series to...
In(z) 3, Consider the function f(x)= (a) Find the Taylor series for r(z) at -e. b) What is the interval of convergence for this Taylor series? (c) Write out the constant term of your Taylor series from part (a). (Your answer should be a series!). (d) What can you say about the series you found in part (c), by interpreting it as the limit of your series as x → 0. (Does it converge? If so, what is the limit?)...