
Question 25 For which values of a does the following power series converge? 8 (-1) +...
(13) For what values of x, does the power series 1 n. (2x + 1)^ In 5n n=0 converge? (14) For what values of x, does the power series ^ (n + 1)! nao (2n + 1).X" converge?
number 4
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series cos(x) (2n)! (-« <...
number 4 as clearly as possible
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series...
Question 3 (1 point) The function f is defined by the power series 1)2 3! 5! 72n+1)! 1)% n-0 (2n+1) ! for all real numbers x. Use the first and second derivative test by finding f(x) and f"(x). Determine whether f has a local maximum, a local minimum, or neither at x=0. Give a reason for your answer. Use the
Question 3 (1 point) The function f is defined by the power series 1)2 3! 5! 72n+1)! 1)% n-0 (2n+1)...
Pt 1
pt 2
pt 3
pt 4
Please Answer every question and SHOW WORK!
Determine whether the series n-1 Σ (2n)! 2". (2n! converge or diverge 1. both series converge 2. only series II converges 3. only series I converg es 4. both series diverge Determine whether the series 2! 1515.9 1-5.9-13 3! 4! 7m 1.5.9..(4n -3) is absolutely convergent, conditionally con- vergent, or divergent 1. conditionally convergent 2. absolutely convergent 3. divergent Determine which, if any, of the...
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
12. For what values of r does the series (2n)!r" 22n(n!) converge absolutely? converge conditionally? diverge? n=1
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't forget to state the tests from class that you are using!). If any of the convergent ones can be evaluated by the techniques we have learned in class, you should give their value as well. 4 + 3n" + 7n +2 In(In(n)) (1) Σ 3n13 - 2n° +58 +n +3 4n In(n) (ii) 16
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't forget to state the tests from class that you are using!). If any of the convergent ones can be evaluated by the techniques we have learned in class, you should give their value as well. An: + 3n" + 7n +2 In(In(n)) (1) V3n13 - 2n° +55 +n +3 An In(n) 8] (ii) ns16 Σ (3n)! (n!) 33" (iv)
1. Determine if the following series converge or diverge. If they converge give the value of the series. q-n+24n+1 n=1 37n 2N=14+4n 2 72 C. 271
1. Determine if the following series converge or diverge. If they converge give the value of the series. q-n+24n+1 n=1 37n 2N=14+4n 2 72 C. 271