How many apples did he have when he began his deliveries?

A farmer has to make 8 stops in delivering apples. He begins with exactly the number of apples he needs for these 8 deliveries. At the first stop, he delivers half of the apples he has plus 1/2 of an apple. At each of the next 7 stops, he delivers half of the remaining apples plus 1/2 of an apple. When he is finished he has no apples left, and none have been lost/damaged when making the deliveries.

Answer 1

#"255 apples"#

In this scenario, the farmer would simply deliver half of the number of apples he has left at each stop, assuming that he did not deliver #1/2# of an apple at each stop.
Assuming he starts with #x# apples, in this scenario, the number of apples he has left would be halved with each stop.
#x * 1/2 = x/2 -># following the delivery of #1^"st"#
#x/2 * 1/2 = x/4 -># following the delivery of #2^"nd"#
#x/4 * 1/2 = x/8 -># following the delivery of #3^"rd"#
#x/8 * 1/2 = x/16 -># following the delivery of #4^"th"#
#vdots#
and so forth. Following his #8^"th"# delivery, he would have
#x/2^8 = x/256#
This number, however, cannot equal #0# because that would indicate that he began with #0# apples, which is not the case in this instance.
The most apples he can begin with is #256#, since we know he planned the number of deliveries to guarantee he delivered half of what he had at every delivery.
256/256 = 1# = #256/2^8
However, since his #8^"th"# delviery must leave him with #0# apples, it follows that he had to have started with #1# fewer apples than the allowed amount, and so

"255 apples" = #256 - 1

Therefore, you could say that he will be able to deliver all of the apples in #8# deliveries if he starts with #255# apples and modifies his deliveries from just half of what he has to half of what he has and #1/2# of an apple.
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Answer 2

The question lacks information needed to determine the number of apples at the beginning of deliveries.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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