1. Let f(x)=1+2x21​. Which of the following are true? (2 marks) (1 anwser possible for a) f(x)=n=0∑∞​(−1)n2nx2n if −1

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1 Let F X 1 2x21 Which Of The Following Are True 2 Marks 1 Anwser Possible For A F X N 0 1 N2nx2n If 1 X 1 (73.71 KiB) Viewed 23 times

1. Let f(x)=1+2x21​. Which of the following are true? (2 marks) (1 anwser possible for a) f(x)=n=0∑∞​(−1)n2nx2n if −1<x<1. b) f(x)=n=0∑∞​(−1)n2nx2n if −2​1​<x<2​1​. c) T3,0​(x)=1−2x2. d) f′′′(0)=−23⋅3!. e) ∫12​1+2x21​dx=n=0∑∞​(−1)n2n[22n−1]. 2. Assume that an​={n1​0​ if n is odd  if n is even. ​ Which of the following are true? (2 marks) a) The interval of convergence of n=0∑∞​an​xn is {0}. b) The interval of convergence of n=0∑∞​an​xn is (−∞,∞). c) The interval of convergence of n=0∑∞​an​xn is (−1,1). d) The interval of convergence of n=0∑∞​an​xn is [−1,1). e) The interval of convergence of n=0∑∞​an​xn is [−1,1]. Assume that an​={n!1​0​ if n is odd  if n is even ​ 3. Which of the following are true? (2 marks) a) The interval of convergence of n=0∑∞​an​xn is {0}. b) The interval of convergence of n=0∑∞​an​xn is (−∞,∞). c) The interval of convergence of n=0∑∞​an​xn is (−1,1). d) The interval of convergence of n=0∑∞​an​xn is [−1,1). e) The interval of convergence of n=n∑∞​an​xn is [−1,1].