Ch12 Infinite Sequence and Series

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Ch12Infinite Sequence and Series

• ???????

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• 12.1 ????
• 12.2 ????
• 12.3 ?????
• 12.4 ?????
• 12.5 ????
• 12.6 ??????????????????
• 12.8 ????
• 12.9 ?????????
• 12.10 Taylor ? Maclaurin??

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12.10 Taylor Maclaurin Series

• Taylor ? Maclaurin??

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• ??Taylor ? Maclaurin?????
• ???????Taylor ? Maclaurin ??

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Taylor ? Maclaurin??
?????
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Taylor ? Maclaurin??

• Taylor n????

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Example 1 ex ?Maclaurin??
f(x) ex
f(x) ex
f(x) ex
f (3)(x) ex
f (4)(x) ex
f(0) e0 1
f(0) e0 1
f(0) e0 1
f (3)(0) e0 1
f (4)(0) e0 1
?
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ex ?Maclaurin??
1
1
1
1
1
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Example 3 ex ?Taylor?? a2
f(x) ex
f(x) ex
f(x) ex
f (3)(x) ex
f (4)(x) ex
f(2) e2
f(2) e2
f(2) e2
f (3)(2) e2
f (4)(2) e2
?
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e2
e2
e2
e2
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Example 5 cosx ?Maclaurin??
f(x) cos x
f(x) -sin x
f(x) -cos x
f (3)(x) sin x
f (4)(x) cos x
f(0) cos 0 1
f(0) -sin 0 0
f(0) -cos 0 -1
f (3)(0) sin 0 0
f (4)(0) cos 0 1
?
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Example cosx ?Maclaurin??
1
0
-1
0
1
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cosx ?Maclaurin??
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Example 4 sinx ?Maclaurin??
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?????Maclaurin??
??
??
??
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Example 6 xcosx ?Maclaurin??
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Q 1 cos2x ?Maclaurin??
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Q1 cos2x ?Maclaurin??
2x
2x
2x
2x
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1. ½
2. 1
3. ?
4. 0

Q2

• ??????
• Maclaurins Series

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Example 11
1
1
n-2
0
0
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Q3 e-x ?Maclaurin??
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Example e-x ?Maclaurin??
-x
1
-x
-x
-x
1
1
1
1
-x