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Graphing and Visualizing Limits 1037 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.

Language:
English Language

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

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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