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MATH 1B
QUIZ #4 (Show All Your Work)
NAME:____________________________________
1) Find the radius of convergence and interval of convergence of the following series.
∞
(−1)𝑛−1 𝑛
∑
𝑥
𝑛7𝑛
𝑛=1
2) Find a power series representation for the function and determine the interval of
convergence.
𝑓(𝑥) =
6
2𝑥 + 5
3) Find the Taylor series for 𝑓(𝑥) centered at the given value of 𝑎 using the definition of a
Taylor series.
𝑓(𝑥) = 𝑒 2𝑥, 𝑎 = 3
4) Use the Maclaurin series in Table 1 (pg 768) to obtain the Maclaurin series for the given
function.
𝑓(𝑥) = 𝑥 2 ln (1 + 𝑥 3 )
5) Find an equation of the tangent to the curve at the point corresponding to the given value
of the parameter. Find the second derivative as well.
𝑥 = √𝑡,
𝑦 = 𝑡 2 − 2𝑡; 𝑡 = 4
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