1) (a) Rewrite the expression k-0 as a sum whose generic term involves (b) Determine an...
3. (a) Rewrite the given expression as a sum whose generic term
x . ∞∞
i. x ? nanxn−1 + ? akxk n=1 k=0
∞∞
? n−1 ? n
ii. nanx + x anx n=1 n=0
(b) Determine the an so that the equation
∞∞ ?nanxn−1 +2?anxn =0 n=1 n=0
is satisfied. Try to identify the function represented by the
series
?∞ n n=0 anx .
use differential equations method
ii. narx"-1+ranxa 3. (a) Rewrite the given expression as a...
Rewrite the given expression using a single power series whose general term involves x (x+1)(n-1" n-2 n-2 n-0 k-0 2c, +Co+[(k+1)kc,+(k+2)(k+1)c2 +c,] R-1 k+1+3)k +o} k-0 +1)eo1+( +2)( +1)2 +c]k k-0
Exercise 2. 19 pts Manipulation of sums Rewrite the following series in only one sum whose generic term involves 2", i.e. in the form of Check your answer by writing down the first three nonzero terms! (a) (3 pts) (1-2) Ža(n = 1)emons (b) (3 pts) (c) (3 pts) +] (n = 1)ex**++
Q2-Σ Notation Review notation by investigating In this problem we will remind ourselves of 2k k O a) Consider the similar finite sum 2* k-0 Using n - 3, rewrite this expression in expanded form, and then evaluate it. b) Rewrite Expression (2) in expanded form for n-6, and then evaluate it c) Expression (2) becomes a better approximation to Expression (1) as n grows larger. To get an idea of what (1) is, evaluate (2) using n 100. Don't...
Determine the interval of convergence for the following series. a/ sum (x-3)k / sqrt k from k=1 to infinity b/ sum (-x)k / k! from k=0 to infinity c/ sum (2x - 21)k / k4 from k=1 to infinity
prove that J2(x)=sum from k=0 to infinity [
(-1)^k/2^9@k+2)*k!(k+2)! ]*x^(2k+2) is a solution of the Bessel
differential equation of order 2:
x^2y'' + xy' + (x^2-4)y=0
(-1)4 9- Using the ratio test, one can easily show that the series +2converges for all e R. Prove that (-1)X h(x) = E, 22k +2k!(k + 2)! 22+2 is a solution of the Bessel differential equation of order 2: In(x) is called the Bessel function of the first Remark. In general the function...
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation by H(s) a) D, and find the transfer function for the system above. (5 marks) Sketch the Bode plot. b) (5 marks)
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation...
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...
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also assume that x,y>0 7.1. Derive the marginal utility of x and the marginal utility of y and state whether or not the assumption that more is better is satisfied for both goods. 7.2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x?What does it mean in words? 7.3. What is MRS.y? 7.4. Suppose a, b- Wht...
I need help with question 30d
16. y = 0 (that is, y(x) = 0 for all x, also written y(x) = 0) is a solution of (2) (not of (1) if (x) • o , called the trivial solution 17. The sum of a solution of (1) and a solution of (2) is a solution of (1). 18. The difference of two solutions of (1) is a solution of (2). 19. If yı is a solution of (1), what...