Taylor's Theorem
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1 Write down the Taylor polynomial of , . Use Taylor's theorem to
show that =
2. Given that , 1 < e < 3. Do the followings.
a) Write down the Taylor polynomial of and show that for and
b) Use a) to show that for all c) Conclude that e is irrational?
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Solution Summary
Taylor's theorem are investigated.
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1. Proof:
Let , then , , and so on.
In general, we have . By Taylor's Theorem, we expand at and get . Especially, set , we have
.
2. Proof:
(a) Let , then and thus . By Taylor's Theorem, we ...
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