Can you please do number 5 586 CHAPTER 8 Infinite Series In e In exercises 1-40,...
please answer all the questions. just rearranging. Explanation is not needed. Use modular arithmetic to prove that 3|(221 – 1) for an integer n > 0. Hence, 3|(221 – 1) for n > 0. To show that 3|(221 – 1), we can show that (221 – 1) = 0 (mod 3). We have: (221 – 1) = (4” – 1) (mod 3) Then, (22n – 1) = (1 - 1) = 0 (mod 3) Since 4 = 1 (mod 3),...
Please answer Exercises 1 1.1 Thinking about your own u functioin Here is a question we could ask you indifferent between having 5k for sure and having 1 k with probability π1 and 10k with probability (1- T). Suppose person n answers Ti-.3. If we interpret that answer in terms of expected utility, then we have the equation person n. For what magnitude of πι are where the second equality comes from the normalization, un (1k)0 and Having determined that...
please do a,b,c,d, j, k ,m ,r,s Exercise 5.12. Determine whether the infinite series is convergent, of vergent. Show your reasoning. In particular, make clear which of the several available tests you are using. X 0 ΣΠΗ3 ο Στη + 1)(n + 3) 4) Στ+6 η2 + 5η +6 Stainle 3( +1)/2 4ก 2 10” 8 80 81 82 8 ก+ 7 ๑int 18 ปี 2) ") oth) 18 มี 18 ก ! Exercise 5.12. Determine whether the infinite series...
Solve number 3 with good details. Please do not use other's work. 1. Solve the equation 2. Prove that the series 00 n 2 converges at all points of the unit circle ll-1, except -1 3. Show that there is no convergent power series f(z)- 2, such that f (z) 1 forz 1/2, 1/3, 1/4,... and f(0) 0 l<
(1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV If it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA...
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
I need help with Question 1.63. Thank You!! 35 Additional Exercises for Chapter 1 1.63. List the elements of the set S = {(x, y) e Z × Z: |x|+ \y| = 3). Plot the corresponding points in the Euclidean xy- plane. 1.64. For A = {1, 2} and B 1.65. For A = {x e R: |x – 1| < 2} and B = {y e R: ly – 4| < 2), give a geometric description of the points-...
1,2,3, and 4 Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Number 8, 9, 13 please dow Help XMA 220 Homework XYuzu: Calculus: Early Transcen + 638/4/[email protected]:2.22 ים: İIO Using the Direct Comparison Test In Exercises 5-16, use the Direct Comparison Test to determine the convergence or divergence of the series. 5. 6. 2n-1 4" 7. 8. oo In n 9. 10. 1l 14, Σ 5"1 n=0 15. Sin n 16. Σ cos n +2 /n 回,回Using the Limit Comparison Test In Exercises 17-26, use the Limit Comparison Test to determine...
Differential equation Q5 please / Q10 if possible, thank you so much Exercises 1. Show that L{cos kt) = s22 for s> 0. 2. Euler's formula elkcos kt+i sin kt can be used to obtain an additional formula cos kt(ek+e-ik), Show that the result of Exercise 1 can now be obtained with a formal application of the Laplace transform. 3. Obtain the transform for sin kt by an argument similar to the one suggested in Exercise 2 4. Evaluate L(r2...