Question
The Taylor theorem can depict in the following format
Question 7Answer
a.
f
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x
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=
P
n
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x
y
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+
R
n
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x
y
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b.
f
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=
P
n
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x
y
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-
R
n
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x
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c.
f
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=
P
n
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+
R
n
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x
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d.
f
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=
P
n
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x
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-
R
n
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Question 7Answer
a.
f
(
x
)
=
P
n
(
x
y
)
+
R
n
(
x
y
)
b.
f
(
x
)
=
P
n
(
x
y
)
-
R
n
(
x
y
)
c.
f
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x
)
=
P
n
(
x
)
+
R
n
(
x
)
d.
f
(
x
)
=
P
n
(
x
)
-
R
n
(
x
)
Answers
GPT-4o mini
The correct statement of the Taylor theorem in a typical format is:
**c.** \( f(x) = P_n(x) + R_n(x) \)
In this expression:
- \( f(x) \) is the function being approximated.
- \( P_n(x) \) is the nth-degree Taylor polynomial of \( f \) at some point (often around \( a \)).
- \( R_n(x) \) is the remainder term which accounts for the error in using the polynomial to approximate \( f(x) \).
Thus, the answer is **c**.
**c.** \( f(x) = P_n(x) + R_n(x) \)
In this expression:
- \( f(x) \) is the function being approximated.
- \( P_n(x) \) is the nth-degree Taylor polynomial of \( f \) at some point (often around \( a \)).
- \( R_n(x) \) is the remainder term which accounts for the error in using the polynomial to approximate \( f(x) \).
Thus, the answer is **c**.