Lagrange Error Bound
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Compute
R
1
(
x
)
R_1(x)
R
1
(
x
)
for
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
at
x
=
0.1
x = 0.1
x
=
0.1
,
a
=
0
a = 0
a
=
0
.
QUESTION
What is the error bound for
f
(
x
)
=
x
4
f(x) = x^4
f
(
x
)
=
x
4
at
x
=
0.1
x = 0.1
x
=
0.1
,
a
=
0
a = 0
a
=
0
,
n
=
3
n = 3
n
=
3
?
QUESTION
Evaluate
R
2
(
x
)
R_2(x)
R
2
(
x
)
for
f
(
x
)
=
e
x
f(x) = e^x
f
(
x
)
=
e
x
at
x
=
0.2
x = 0.2
x
=
0.2
,
a
=
0
a = 0
a
=
0
.
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ANSWER
R
2
(
0.2
)
=
e
0.2
(
0.2
)
3
3
!
R_2(0.2) = \frac{e^{0.2} (0.2)^3}{3!}
R
2
(
0.2
)
=
3
!
e
0.2
(
0.2
)
3
. The third derivative of
e
x
e^x
e
x
is
e
x
e^x
e
x
, maximum at
x
=
0.2
x = 0.2
x
=
0.2
.
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