#### SusanCoutu

##### New member

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Thanks for any help!

- Thread starter SusanCoutu
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Thanks for any help!

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This is a topic of face-to-face discussion. It is very hard to explain through "posts" - at least for me.

Thanks for any help!

For the time being - just take it for granted.

Ask this question to your teacher and have a face-to-face discussion with the teacher.

Before that brush-up your concept of limit - thoroughly.

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Let's abandon that concept and truly attempt to understand the Calculus. If the derivative or the integral is just an approximation, then you do not understand the limit - you stopped before you actually found the limit. We sometimes use words like "in the limit" or "at the limit" or "take the limit". These are okay, but not perfect. The simplest example to understand is the common question:

Is 0.99999.... EQUAL to one (1), or is it just an approximation of one (1)? Maybe really, REALLY close?

Well, if "..." means you just keep going, then it IS EQUAL to one (1). If you stop, somewhere, anywhere, then it is only an approximation. I like to think of it with this question: If 0.999..... is NOT EQUAL to one (1), then how far from one (1) is it? You cannot supply a meaningful answer.

Definitely a question for a face-to-face. Giving up finite thinking isn't usually easy. You'll get it.

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I would reverse what you say: an actual marginal [rate of] change is only an approximation to the derivative!the derivative of a function is only a very close approximationto the actual marginal change of the function, provided dx is very small compared to dy, then shouldn't any integrals arrived from the derivative by using integration be only an approximation as well of the function the derivative was originally supposed to represent? My textbook seems to suggest that an integral arrived at by using antidifferentiation is indeed the true antiderivative and thus it's a perfect description of any measurement of total change, but I just find it hard to wrap my head around how it should be possible to arrive at the original by reversing only an approximation. Maybe my understanding of this is flawed.

Thanks for any help!

The derivative, thought of as the slope of a curve at a point, is the

Similarly, the definite integral, thought of as the area under a curve, is the

This is why calculus is so powerful!

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Funny story: Stoners keep stealing Mile Marker "420" from highways. I've seen stories from at least Oregon and Colorado where they have replaced "420" with "419.99" or "419.99..." in an effort to end the theft. Someone in the highway department is definitely thinking about the problem. Their notation might not always be right, but I think it's pretty funny. Math in the real word I think we call that.

If they put "419.99" at 419.99, then it's exactly right.

Funny story: Stoners keep stealing Mile Marker "420" from highways. I've seen stories from at least Oregon and Colorado where they have replaced "420" with "419.99" or "419.99..." in an effort to end the theft. Someone in the highway department is definitely thinking about the problem. Their notation might not always be right, but I think it's pretty funny. Math in the real word I think we call that.

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Indeed. I have not seen any "we also moved he sign 52.8 ft from it's previous location" or any follow up to suggest the technique was effective in preventing theft.If they put "419.99" at 419.99, then it's exactly right.