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sammy [17]
3 years ago
9

A box of chocolates contains, on average, 12 pieces of chocolate. If the number of chocolates in each box never varies from the

average by more than three, what is the least number of chocolates that will be contained in four boxes? A. 3 pieces B. 4 pieces C. 36 pieces D.12 pieces
Mathematics
1 answer:
marta [7]3 years ago
3 0
The answer would be C. 36 
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3 years ago
If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.
Pie
Given that f^{(n)}(0)=(n+1)!, we have for f(x) the Taylor series expansion about 0 as

f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n

Replace n+1 with n, so that the series is equivalent to

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and notice that

\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}

Recall that for |x|, we have

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which means

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5 0
3 years ago
Let
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