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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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