questions are all in the pdf. I need this in one hour! Thank you.
QUIZ #4 (Show All Your Work)
1) Find the radius of convergence and interval of convergence of the following series.
2) Find a power series representation for the function and determine the interval of
2𝑥 + 5
3) Find the Taylor series for 𝑓(𝑥) centered at the given value of 𝑎 using the definition of a
𝑓(𝑥) = 𝑒 2𝑥, 𝑎 = 3
4) Use the Maclaurin series in Table 1 (pg 768) to obtain the Maclaurin series for the given
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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