4 4. Answer the following questions. Justify your answers. A. (Spts) Determine if the series 2.0...
1. Answer the following questions. Justify your answers. a. (8pts) Find the Taylor series for f(x) = (5x centered at a = 1 using the definition of the Taylor series. Also find the radius of convergence of the series. b. (8pts) Find a power series representation for the function f(x) = 1 5+X C. (4pts) Suppose that the function F is an antiderivative of a function f. How can you obtain the Maclaurin series of F from the Maclaurin series...
Help 5. Answer the following questions. Justify your answers. A. (8pts) If the nth partial sum of a series an is equal to sn = (1+0)") what is the sum of the series? en B. (8pts) Determine if the series 2n=1zten is convergent or divergent. C. (4pts) Can you make an infinite series of nonzero terms that converges to any number you want? Explain.
Help 1*4 2. Answer the following questions. Justify your answers. A. (&pts) Find the radius and interval of convergence of the series X=1 9, B. (Spts) Find the radius and interval of convergence of the series X=1 C (4pts) If the radius of convergence of a power series cux" is R, what is the radius of convergence of the power series Eco(5x)" ? Show your work.
1. Answer the following questions. Justify your answers. (a) (3 marks) For what values of x does the series 1 + 22x 2 + 24x 4 + 26x 6 · · · + 22nx 2n + · · · converge? (b) (9 marks) Is the following series absolutely convergent, conditionally convergent or divergent? i. X∞ n=1 2 √ n − 2 √ n + 1 ii. X∞ n=1 arctan(n) n2 + 1 iii. X∞ k=1 (−1)k k 1. Answer the...
4. Answer the following questions. Justify your answers. a. Is the Ratio Test always conclusive? If not, give an example of a series for which the Ratio Test is inconclusive. b. Determine if the series En=1 an is convergent or divergent.
(1 point) We will determine whether the series n3 + 2n an - is convergent or divergent using the Limit Comparison Test (note that the Comparison Test is difficult to apply in this case). The given series has positive terms, which is a requirement for applying the Limit Comparison Test. First we must find an appropriate series bn for comparison (this series must also have positive terms). The most reasonable choice is ba - (choose something of the form 1/mp...
5. (15 pts) Sinn a.) Apply the Divergence Test to this series. State your conclusion b.) Apply the Integral test. You should state the three conditions needed for c) but you may skip if possible, otherwise, say "no sum. 6. (20 pts) _ ( +1) a.) Determine converge diverge using one of the comparison tests. Justify every step b.) Find the correct partial fraction decomposition for a = Solve for the unknown constants in that partial fraction decomposition. C.) Rewrite...
4. (a) Indicate where the series is (i) absolutely convergent, n-1 where it is (ii) conditionally convergent, and where it is (iii) divergent. Justify your answers Find f,(z) if f(x) = arctan (e* ) + arcsin V2x + 4. (b) (a) Set up (but do not evaluate) a definite integral that represents the area 5. of the region R inside the circle r = 4 sin θ and outside the circle r = 2. Carefully sketch the region R. (i)...
Determine whether the following series converge or diverge. Fully justify your answer. T(-1)"(n? – 2n) 400n3 + 78972 2
All three questions Determine whether the following series converge or diverge. Show your work and explain your reasoning. If a series converges, say what it converges to (if possible). Problem 1. Ln(Inn) Problem 2. n=3 nv n2 - 1 $ (-1)"8" Problem 3. 52n