CAS MA 124 Study Guide - Midterm Guide: Ion, Binomial Series
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MA 124 - Fall ’12 - Exam 3A
GENERAL INSTRUCTIONS: Show all your work. A correct answer without justiﬁ-
cation receives no credit. Check your algebra and arithmetic carefully.
1) (16 points)
a) (10 points) Use the fact that
to ﬁnd a power series for
f(x) = 1
b) (6 points) What is the interval of convergence of the series you obtained in a) ? Justify
2) (16 points) Use the binomial series
(1 + x)p=
to ﬁnd an inﬁnite series that gives the exact value of
√1 + x6dx .
Write out the ﬁrst three non-zero terms of this series.
3) (16 points)
a) (4 points) Find the Taylor polynomial p2(x) of degree 2 and center 0 for the function
f(x) = ln(1 + x)
b) (4 points) Use p2(x) to write an approximate value for
c) (4 points) Write the remainder term R2(x) for f(x) = ln(1 + x) and a= 0.
d) (4 points) Use your expression in c) to estimate the maximum absolute error of your
approximation in b).