Please help me to prove this proposition! Thanks a lot!
Please help me to prove this proposition! Thanks a lot! Proposition Let fi, f2 be power...
Please help me. these go together. if you help then i will definitely rate!:) (a) Use the power series for 1 to prove that the Taylor series centered at x = 0 for In(1+x) is 1+1 + (-1)" 2"41 2 3 4 5 7+1 (b) The Taylor series centered at 1 = 0 for In (1+1) given in part (a) converges to In(1+1) on its interval of convergence. Let g(x) = (x - 3)2 In 1 + Write the Taylor...
I need help on questions 17, 21, and 25. Thanks! In Exercises 9-24, a power series is given. (a) Find the radius of convergence. (b) Find the interval of convergence. 17. Σvnx n=0 18. Σ n=0 19. 31 (x – 5)" n! n=0 20. Σ(-1)"n!(x – 10) n=0 21. η2 n=1 In Exercises 25 – 30, a function f(x) = ax" is given. (a) Give a power series for f'(x) and its interval of conver- gence. (b) Give a power...
please help to solve this differential equation. 3. Use power series solutions to solve (x+1)y"+(x-2)y' +y = 0. Center the power se- ries about the ordinary point o = 0. Write the solution as y = col first four terms..]+ ciſfirst four terms...). 4. Find the minimum radius of convergence for a power series solution to the ODE (22+2x+5)/' +10y = 0 centered about the ordinary point Xo = -6
I need help solving these problems 1. Suppose that y= a (x-1)" is the power series solution of the following initial value problem. x-y+2y=0; y(t) = -2, y(1)=1 Find the value of az. 2. Suppose that y=0(x) is the solution of the following initial value problem. y" + xy - (sinx)y=0; y(0)=1, 7(0) = 3 Find the value of (0) 3. Let p be the radius of convergence for the Taylor series of the following rational function centered at the...
please help me! Thanks in advance :) 5. Let N be a Poisson random variable with parameter λ Suppose ξ1S2, is a sequence of 1.1.d. random variables with mean μ and variance σ2, independent of N. Let SN-ξι 5N. Determi ne the me an and variance of Sw. 6. Let X, Y be independent random variables, each having Exponential(A) distribution. What is the conditional density function of X given that Z =
Please help with the abstract algebra question detaily. Thanks. 1. Suppose r E Q. Let β cos(m). Prove that β is algebraic over Q. Let E-Q(3). Prove that Q(3) is a normal extension of Q and that Gal(E/Q) is an abelian group. 1. Suppose r E Q. Let β cos(m). Prove that β is algebraic over Q. Let E-Q(3). Prove that Q(3) is a normal extension of Q and that Gal(E/Q) is an abelian group.
Please help me with the last part of the question. I need steps. Thanks a lot. Suppose you are the manager of a watchmaking firm operating in a competitive market. Your cost of production is given by C = 100 + 2q², where q is the level of output and C is total cost. (The marginal cost of production, MC(q), is 4q; the fixed cost, FC, is $100). If the price of a watch is $80, how many watches should...
plz help me analysis question! Thanks in advance 5. For each n є N let fn : R R be given by f,(x)-imrz. Prove that the sequence {f. of functions converges pointwise to the function f R- R given by 1+nr if x#0 f(x)-0 5. For each n є N let fn : R R be given by f,(x)-imrz. Prove that the sequence {f. of functions converges pointwise to the function f R- R given by 1+nr if x#0 f(x)-0
Could you help me with 11,12,and 13 please ? Thanks in advance, Massimo Ulto 8. If you have had calculus, prove the power rule for positive exponents. Specifically, prove that for every positive integer n, (x") = na"-1. (Hint: Use induction on n and the Product rule, writing " = 9. Prove that for every positive integer n n(n + 1 + 2 + ... +n= 10. Prove that for every positive integer n. 12 +22+... 2 n(n + 1)(2n...
Hi there, is this possible to give me a help on this probability question, literally in a desperate situation! Thanks a lot! Problem 4 (20p). Let α > 0, and for each n N let Xn : Ω R be a random variable on a probability space (Ω,F,P) with the garnma distribution Γαη. Does there exist a random variable X:S2 → R such that Xn → X as n → oo? Problem 4 (20p). Let α > 0, and for...