Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
T
n
(
x
)
T_n(x)
T
n
(
x
)
be the
n
n
n
th-degree Maclaurin polynomial for
e
2
x
e^{2x}
e
2
x
. For all
x
x
x
in
[
−
0.2
,
0.2
]
[-0.2,0.2]
[
−
0.2
,
0.2
]
, what is the least integer
n
n
n
that guarantees the relative error
∣
e
2
x
−
T
n
(
x
)
e
2
x
∣
\displaystyle \bigl|\tfrac{e^{2x}-T_n(x)}{e^{2x}}\bigr|
e
2
x
e
2
x
−
T
n
(
x
)
is less than
1
×
10
−
4
1\times10^{-4}
1
×
1
0
−
4
? a)
n
=
3
n=3
n
=
3
b)
n
=
5
n=5
n
=
5
c)
n
=
4
n=4
n
=
4
d)
n
=
7
n=7
n
=
7
Browse the problem library