Finding Taylor Polynomial Approximations of Functions
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
What is the
3
r
d
3^{rd}
3
r
d
degree Taylor polynomial for
f
(
x
)
=
arcsin
(
x
)
f(x) = \text{arcsin}(x)
f
(
x
)
=
arcsin
(
x
)
at
x
=
0
x = 0
x
=
0
?
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
?
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ANSWER
0
−
(
x
−
π
)
0 - (x-\pi)
0
−
(
x
−
π
)
.
sin
(
π
)
=
0
\sin(\pi)=0
sin
(
π
)
=
0
,
sin
′
(
π
)
=
−
1
\sin'(\pi)=-1
sin
′
(
π
)
=
−
1
gives linear term.
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