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AP Calculus: Problem Explanation Limits Drill 1, Problem 1. Which of the following are true about the pictured function?
Breathe in deeply through the nose... Now slowly exhale... Breathe in... And out... Now visualize the graph of the limit of f(x) as x approaches 2....
AP Calculus 1.4 Limits. Given the limit, which of the following are true?
Graphing and Visualizing Limits 1040 Views
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Description:
Breathe in deeply through the nose... Now slowly exhale... Breathe in... And out... Now visualize the graph of the limit of f(x) as x approaches 2. Sorry, but if you're looking for serious meditation and relaxation, check into a day spa.
Transcript
- 00:03
graphing and visualizing limits a la shmoop [Girl visualising graphing and limits]
- 00:07
big Randy used to be a sumo wrestler in the eighties so he decides to write a
- 00:12
guide on how to get that sumo body for the youngsters who want to be the next [Randy holding championship belt]
- 00:17
generations big Randy, his secret was eating doughnuts by the box but he's
- 00:22
forgotten how many boxes he needs to eat to get to a certain weight he decides to
Full Transcript
- 00:27
relive his glory days and find an equation that models his weight gain he
- 00:32
decides to set X as the number of doughnut boxes he eats and Y as the number of
- 00:38
pounds gained he decides that if he's gonna try to help out every aspiring [Young boy by a sumo circle and Randy appears]
- 00:42
sumo wrestler he's gonna need a lot of data so he
- 00:46
sells his 24 karat gold two-piece wrestling suit that he won in the World
- 00:50
Championships of 85 and buys a thousand boxes of donuts and graphs his weight [Randy surrounded by doughnut boxes]
- 00:56
gain after each box he makes it through the whole batch and checks his results
- 01:01
looks like he forgot to record his weight after 200 boxes and 600 boxes
- 01:06
instead of doing his experiment all over again and buying another thousand donut
- 01:10
boxes he decides to use something called limits to estimate his weight gain at
- 01:15
those missing points here's what big Randy's graph currently looks like [Person points at missing data on graph]
- 01:19
notice the missing points called holes at x equals 200 and the jump at x equals
- 01:26
600 let's start by figuring out the hole at x equals 200 his weight gain at 200
- 01:32
can be estimated by the Y value that corresponds to the graph when X is
- 01:36
really really close to 200 which is called a limit at x equals 199 his
- 01:43
weight gain was 49.8 pounds at x equals 301 his weight gain
- 01:48
was 50.2 pounds it looks like the limit as X approaches
- 01:53
200 boxes of donuts is about 50 pounds note that we did this even though the [Graph and young boy appears]
- 01:59
graph is discontinuous and technically didn't have a value at that point we
- 02:04
just guessed we can try to find the limit of a function at any x value [Woman teaching students about x value]
- 02:09
here big Randy only cares about the limit of the graph at x equals 200 and
- 02:13
600 boxes, now let's look at the jump at 600 boxes a limit requires that the Y
- 02:20
values are the same going from x values greater than or less than the x value in
- 02:25
question in this case 600 at 599.99
- 02:29
boxes his weight gain was 98.9 pounds and at 600.01
- 02:34
boxes his weight gain was a 110 pounds it might look like
- 02:39
the weight gained at six hundred boxes could be a hundred to 105 or even 108
- 02:43
pounds but the problem is there is such a small space between 599.99
- 02:47
and 600.01 that there's only [Boy discussing weight gain]
- 02:51
one space for a single value in other words the values at 599.99
- 02:56
and 600.01 boxes need to be
- 03:00
almost the same like at two hundred or the limit to exist
- 03:05
so at 600 the limit does not exist well what does that mean it means that [Question marks appear by the graph]
- 03:11
something wacky we must have happened at box 600 it's all coming back to him now
- 03:15
he forgot to record the gallon of milk he drank with his 600th box of doughnuts [Randy with a gallon of milk and box of doughnuts]
- 03:20
sorry Randy.....
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