Finding Taylor Polynomial Approximations of Functions
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find the
3
r
d
3^{rd}
3
r
d
degree Taylor polynomial for
f
(
x
)
=
ln
(
1
+
x
)
f(x) = \text{ln}(1+x)
f
(
x
)
=
ln
(
1
+
x
)
centered at
0
0
0
.
QUESTION
What is the
2
n
d
2^{nd}
2
n
d
degree Taylor polynomial for
f
(
x
)
=
sin
(
x
)
f(x) = \text{sin}(x)
f
(
x
)
=
sin
(
x
)
centered at
π
\pi
π
?
QUESTION
State the first four terms of the Taylor series for
cosh
(
x
)
\cosh(x)
cosh
(
x
)
centered at
0
0
0
.
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ANSWER
1
+
x
2
2
!
+
x
4
4
!
+
x
6
6
!
1 + \frac{x^2}{2!} + \frac{x^4}{4!} + \frac{x^6}{6!}
1
+
2
!
x
2
+
4
!
x
4
+
6
!
x
6
. Even powers only, like cosine but hyperbolic.
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