MATH 436 - Exam 1 NAME: _________________________
SHOW ALL WORK
1) Let y = f(x) = x cos(.1
x
e
) on the interval [0,
π
].
a) Find the 3rd Taylor polynomial P
)
(
3
x
to f(x) centered at x = 2, and graph both f(x) and P
)
(
3
x
on this interval.
b) What is the total absolute error in this approximation on this interval?
c) Graphically find the "largest" interval containing x = 2 so that this Taylor polynomial will
approximate f(x) with pointwise absolute error of at most .05.
2) Using the remainder formula, find the "smallest" order n so that the Taylor polynomial Pfor f(x) =
sin(2 x) centered at x = 0 will approximate f(x) on the interval [0, 2
π
] with pointwise absolute error in
this approximation of at most .03.
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3) Give some of the advantages and disadvantages of using the methods of Newton 1st order,
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- Spring '08
- Ken
- Math
-
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