Lagrange Error Bound Worksheet With Answers- Calculus Maximus Ws 9.5 Page 3
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13Calculus Maximus
WS 9.5: Lagrange Error Bound
3. Let f be a function that has derivatives of all orders for all real numbers x. Assume that
f
5
6
,
(4)
f
5
8
,
f
5
30
,
f
5
48
, and
f
x
75
for all x in the interval 5,5.2 .
(a) Find the third-degree Taylor polynomial about
for f x .
x
5
(b) Use your answer to part (a) to estimate the value of
f
5.2
. What is the maximum possible error in
making this estimate? Give three decimal places.
(c) Find an interval
, a b such that
a
f
5.2
b . Give three decimal places.
(d) Could
f
5.2
equal 8.254? Show why or why not.
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