Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
T
5
(
x
)
=
x
−
x
3
3
!
+
x
5
5
!
T_5(x)=x-\dfrac{x^3}{3!}+\dfrac{x^5}{5!}
T
5
(
x
)
=
x
−
3
!
x
3
+
5
!
x
5
be the 5th–degree Maclaurin polynomial for
sin
x
\sin x
sin
x
. For what largest symmetric interval about
x
=
0
x=0
x
=
0
does
T
5
(
x
)
T_5(x)
T
5
(
x
)
approximate
sin
x
\sin x
sin
x
with an error less than
10
−
7
10^{-7}
1
0
−
7
? a)
∣
x
∣
≤
0.40
|x|\le 0.40
∣
x
∣
≤
0.40
b)
∣
x
∣
≤
0.32
|x|\le 0.32
∣
x
∣
≤
0.32
c)
∣
x
∣
≤
0.28
|x|\le 0.28
∣
x
∣
≤
0.28
d)
∣
x
∣
≤
0.22
|x|\le 0.22
∣
x
∣
≤
0.22
Browse the problem library