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
2 years, 4 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

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.

Eli Ross Staff - 2 years, 4 months ago

Log in to reply

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?

Ian Bowen - 2 years, 4 months ago

Log in to reply

I'm not Eli, but...

What vertical axis? Do you mean the horizontal axis?

Pi Han Goh - 2 years, 3 months ago

Log in to reply

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

Ian Bowen - 2 years, 3 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...