(1 point) Write out the first four terms of the Maclaurin series of f (x) if f(0) = 15, f' (0) = -3, f"(0) = 12, f"(0) = -13 f ( x ) = + ...(1 point) Find the first five non-zero terms of Taylor series centered at x = 2 for the function below. f (x) = ex Answer: f (x) = 1 + (1/(1!))x + (1/(21))x^2 + (1/(3!))x43 + (1/(4!))x^4 + ... What is the radius of convergence? Answer: R = |Entered Answer Preview Result -1 -1 incorrect 0.333333 correct (-2,-1.33333] (- 2, correct At least one of the answers above is NOT correct. (1 point) Consider the power series (-1)"(3x + 5)" 1= 1 Vn + 2 Find the center and radius of convergence R. If it is infinite, type "infinity" or "inf". Center a = -1 Radius R = 1/3 What is the interval of convergence? (-2, -4/3] Give your answer in interval notation.(1 point) Suppose that _ ,=( Cnx" converges when x = -5 and diverges when x = 6. Determine whether the following series converge or diverge. Answer "Converges" or "Diverges." ? 1. > Cn 7=0 ? v 2. > Cn2" 1=0 ? v 3. > Cn(-8)" n=0 ? 3. [(-1)" Cn 12 n=0(1 point) Find all the values of x such that the given series would converge. 6" (x - 7)" n +7 Answer: Note: Give your answer in interval notationResults for this submission Entered Answer Preview Result (-3, 1) (-3, 1) correct -2 -2 incorrect At least one of the answers above is NOT correct. (1 point) Consider the following series. Answer the following questions. (x + 1)n IM: 1. Find the values of x for which the series converges. Answer (in interval notation): (-3, 1) 2. Find the sum of the series for those values of x. Sum: -2