但是是英文Assume that the volume discounts in Table 1 apply only

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但是是英文
Assume that the volume discounts in Table 1 apply only to that portion of the volume in each
interval.
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For instance,the discounted price for a $4,000 purchase would be computed as follows:
300 + 0.97(700) + 0.95(2,000) + 0.93(1,000) = 3,809
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1.If x is the volume of a purchase before the discount is applied,then write a piecewise definition
for the discounted price P (x) of this purchase.
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2.Use one sided limits to investigate the limit of P(x) as x approaches $1,000.Also,as x
approaches $3,000.
3.Compare this discount method with the one in Question 1.Does one always produce a lower
price than the other?Discuss.(In your discussion you should include a graph of both P(x)
and D(x).)
最好是有解题步骤的

If x≤$300,then D(x)=x;If $300<x≤$1000,then D(x)=0.97x;If $1000<x≤$3000,then D(x)=0.95x;If $3000<x≤$4000,then D(x)=0.93x; limit P(x) =300+ 0.97*700=979 x→$1,000 limit P(x) =300+ 0.97*700+ 0.95*2, 000=2879 x→$3,000no.

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