Lagrange Error Bound Worksheet With Answers- Calculus Maximus Ws 9.5 Page 10
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13Calculus Maximus
WS 9.5: Lagrange Error Bound
1
2
x
13. (Review) Use series to find an estimate for
I
e
dx that is within 0.001 of the actual value.
0
Justify.
14. The Taylor series about
x
5
for a certain function f converges to f x for all x in the interval of
convergence. The nth derivative of f at
x
5
is given by
n
1
n
!
1
n
f
5
and
f
5
.
n
2
2
n
2
Show that the sixth-degree Taylor polynomial for f about
x
5
approximates
f
6
with an error less
1
than
.
1000
Page 10 of 13
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