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This is class quiz. Its from Calculus class. Some key points are: Interval, Convergence, Infinite Series, Endpoints, Power Series, Representation, Arctan
Typology: Exercises
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QUIZ 10
Show ALL your work CAREFULLY.
(a) Find the interval of convergence of the following infinite series [Do not forget to check the endpoints!].
∑^ ∞
k=
(4x)k k^2
(b) Recall that 1 1 − t = 1 +^ t^ +^ t
(^2) + t (^3) + t (^4) + ... for |t| < 1.
Use this to obtain a power series representation of arctan x. [What is the derivative of arctan x?]
(c) Use (b) to evaluate limx→ 0 arctanx x.
Date: April 4, 2008. 1
