Lagrange Error Bound Worksheet With Answers- Calculus Maximus Ws 9.5 Page 6
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13Calculus Maximus
WS 9.5: Lagrange Error Bound
9. Let f be a function that has derivatives of all orders on the interval
1,1 . Assume
f
0
1
,
1
1
3
4
f
0
,
f
0
,
f
0
, and
f
x
6
for all x in the interval
1,1 .
2
4
8
(a) Find the third-degree Taylor polynomial about
x
0
for the function f.
(b) Use your answer to part (a) to estimate the value of
f
0.5
.
(d) What is the maximum possible error for the approximation made in part (b)?
Page 6 of 13
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