Is the "amount of perfume in a bottle" discrete or continuous? Why?

Answer 1

Continuous.

“Discrete” means that something can only take on particular, unique, step changes in value. “Continuous” means that the value can take on any value within a particular range. So, any liquid can be put into a bottle at any amount until the bottle is full. The value (amount) of liquid in the bottle can change continuously.

In contrast, the number of apples in a bag is a discrete number (normally). We do not allow for “partial apples”, much less a continuous value of “apple”. There is either another one or more, or less. The value of the number of apples in the bag may be changed, but the amount is always discrete – whole increments with a gap between them.

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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.