We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
6. Suppose f(x) is the power series f(x) = § ((x – 3)*. k=1 (a) What...
n=0 (5 points each) Suppose the power series an(x - 1)" converges for 1 = 4 and diverges for x = -4. Answer each question below as yes, no, or can not be determined. (a) Does the power series converge for x = -1? (b) Does the power series converge for x = -2? (c) Does the power series converge for x = 5? (d) Does the power series converge for x = 7?
k=1 Question 4. Suppose that the power series ax (x – 2)* converges at x = 5 and diverges at x = -7. Write four real numbers at which the series converges and two real numbers at which the series diverges. What can you say about the radius of convergence? Explain your answers clearly.
NO Question # 3. (3 marks) Consider the power series, f(x) = Žan(x+1)". Suppose we know that f(-4), as a series, diverges, while f(2) converges. Determine the radius of convergence of the power series for f'(). Precisely name the results we learned in Week 3 that you use, and where you are using them.
Σ (-1)n(7x+6 ,- Consider the series (a) Find the series' radius and interval of convergence (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally? (a) Find the interval of convergence Find the radius of convergence (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in...
Determine for what values of x the power series (-1)"2"(x+1)" converges. 3"n What is the interval of convergence? What is the center? What is R the radius of convergence?
please i need the question 9 and 10 for the detailed proof and
explaination ! thanks !
akx*, then for what values does the series 9. If R is the radius of convergence for Σ000 Σ000Akx-k converge? Explain. 10. Suppose that the series Σ ak of real numbers converges conditionally. Prove that the power series Σ001 akxk has the radius of convergence R = 1
akx*, then for what values does the series 9. If R is the radius of...
0 Question # 3. (3 marks) Consider the power series, f(x) = 3 an(x + 1)". Suppose we know that f(-4), as a series, diveryes, while (2) converges. Determine the radius of convergence of the power series for f'(x). Precisely name the results we learned in Week 3 that you use, and where you are using them.
11. Circle true or false. No justification is needed. (14 points) (a) If f(x) - o(g(x), and both functions are continuous and positive, then fix dz converges. TRUE FALSE (b) If f(x)- o(g(x)), then f(x)gx)~g(x). TRUE FALSE (c) If the power series Σ an(x + 2)" converges atェ= 5, then it must km0 converge at =-6. TRUE FALSE (d) There exists a power series Σ akz" which converges to f(z)-I on some interval of positive length around FALSE TRUE (e)...
6. Suppose Σχο akrk converges when x-3 Give 2 other values of x for which Σ , akrk uppose Ž 0 aka.. converges when x = must converge. 8 7. Indicate if the following are always true or may be false (a) If lim a 0, then Cay converges. (b) If ak > bk 2 0 and Σ bk diverges, then Σ ak converges. (c) If ak > 0 and 'lim k-0, then Σ ak converges (d) If ak >...
-gok Suppose k f (x) = k +1 k=1 (a) Find the radius and interval of convergence of the above power series. (b) Find the power series for f'(x). (c) Find the power series for S* f (x) dx (d) Find f(3) (0) (e) Find the first three nonzero terms of the power series for (f (x))2 (f) Find the function f (x).