Slide 3 of the Calculus Course, Indeterminate Forms Section

Hello everyone,

On the third slide of the the indeterminate forms sector of the calculus course (see here: https://brilliant.org/practice/indeterminate-forms/?p=3), I have two questions about the following text:

'We can’t just define it as “distance divided by time”. What time interval could we use? 1 second? 0.001 second? In the previous situation, no matter how small the interval, for most of it the car will be traveling greater than 30 mph, so will be greater than 30.'

1) When they refer to the time interval, are they referring to a time interval around the point in time that the car's speedometer hits 30 mph? Or are they describing a way to analyze the speed of the car by dividing the distance travelled into "pieces" based on a fixed time interval?

2) When they write that the car will be traveling at a speed greater than 30 mph no matter how small the interval, do they mean that the speed of the car will be greater than 30 mph for most of the time interval around the point in time that the speedometer hits 30 mph? Or do they mean that the car will be traveling at a speed greater than 30 mph for a majority of the total number of fixed time intervals (the "pieces" I mentioned in question 1) over its entire journey?

Note by Ian Bowen
3 years, 3 months ago

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Hi Ian!

We'll get back to you on your questions shortly. In the future, you can always report a problem directly (if you think there's an issue or a point that needs clarification) -- see here for instructions.

Staff - 3 years, 3 months ago

Thanks, Eli. I look forward to the response, and I will use the instructions from link you shared in the future.

Just another quick question, though: What does the vertical axis of the graph on the sixth slide of the same chapter correspond to?

- 3 years, 3 months ago

I'm not Eli, but...

What vertical axis? Do you mean the horizontal axis?

- 3 years, 3 months ago

There is no vertical axis shown, but the graph is two dimensional. So it is a bit confusing.

- 3 years, 3 months ago