find the total energy and total power (average) of the following sequence.
g[k] = A*r^k for k >= 0, and g[k] = 0 for k<0. |r| < 1
use geometric series
find the total energy and total power (average) of the following sequence. g[k] = A*r^k for...
Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series. 1 using fix) 2 g(x)= (1+4x2)2 gix)-ΣΠ k 0 The power series g(x) converges on the interval (Simplify your answer. Type your answer interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) Find the power series representation...
4. Use the power series representaion f(t) = In(1 - 1) =- for -1 <<1, k=1 to find the power series representation for the following function(centered at 0). Give the interval of convergence of the new series. p(r) = 2.r" ln(1-2) 5. Find the power series representation for g centered at 0 by differentiating or integrating the power series of f(perhaps more than once). Give the interval of convergence for the resulting series. 1 using (3) 1-
Consider the power series k=1 (2-x+1)* 2. R . (a) Find the center of convergence of the series. (b) Find the radius of convergence of the series.
Show that the sequence is arithmetic. Find the comm {Cn} = {9-2n} Show that the sequence is arithmetic. d=CH-CH-1 = (9 - 2n) - ( ) (Simplify your answers.) What is the value of the common difference? What is the value of the first term? What is the value of the second term? What is the value of the third term? What is the value of the fourth term? Write out the sum. (k+7) k=1 Find the first second, and...
Find a geometric power series for the function, centered at 0, by the following methods Rx) - 2+x (a) by the technique shown in Examples 1 and 2 Rx) - (b) by long division (Give the first three terms.) Need Help? Read T alk te Tutor - 0/2 points Previous Answers LarCalcET6 9.9.004. Find a geometric power series for the function, centered at 0, by the following methods - 5- (a) by the technique shown in Examples 1 and 2...
the DE 3xy', + (2-x)y'-y-0 and when r-0 С.-Cu-1. When r-1. ck-Ser. For Find two power series solutions to the DE. (points 10) 3 k 1,2,3, both k the DE 3xy', + (2-x)y'-y-0 and when r-0 С.-Cu-1. When r-1. ck-Ser. For Find two power series solutions to the DE. (points 10) 3 k 1,2,3, both k
1. Write down the first few terms of a sequence. How to determine if a sequence is convergent or divergent? 2. Write down the first few terms of a series. Partol sus 3. Tests to determine if a series is convergent or divergent. Divergent Test, Geometric Series Test, Telescopic Series Test, Integral Test, p-series Test, Comparison Test, Limit Comparison Test, Ratio Test, Root Test, Alternating Series Test 4. How to determine whether a series is geometric and whether it is...
Math 181 Worksheets W16 * for <1, to find a power series representation 3. Use the geometric series for the following functions. (a) sw) - (a) f(x) = 1+ 60 Etoje (x)" (b) 9(2) - T- + sa www. in a lot (x)} (14 x 31k (a) Wr) = (e) What are the radii of convergence of the power series above?
11 . 12 13 Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 5 x f(x) = ;- n = 0 Determine the interval of convergence. (Enter your answer using interval notation.) Find a power series representation for the function. (Give your power series representation centered at x = 0.) x2 f(x) X4 + 16 f(x) = Σ |(-1)" ) n = 0 X (a) Use differentiation to find...
Find the power series representation for g centered at O by differentiating or integrating the power series for f(perhaps more than once). Give the interval of convergence for the resulting series g(x) = In (1 - 2x) using f(x) Which of the following is the power series representation for gcentered at 0? LOA 28 Bit OC 1201 NI 883 NI The interval of convergence is (Simplify your answer. Type your answer in interval notation)