ShmoopTube

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graphing and visualizing limits a la shmoop [Girl visualising graphing and limits]

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big Randy used to be a sumo wrestler in the eighties so he decides to write a

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guide on how to get that sumo body for the youngsters who want to be the next [Randy holding championship belt]

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generations big Randy, his secret was eating doughnuts by the box but he's

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forgotten how many boxes he needs to eat to get to a certain weight he decides to

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relive his glory days and find an equation that models his weight gain he

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decides to set X as the number of doughnut boxes he eats and Y as the number of

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pounds gained he decides that if he's gonna try to help out every aspiring [Young boy by a sumo circle and Randy appears]

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sumo wrestler he's gonna need a lot of data so he

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sells his 24 karat gold two-piece wrestling suit that he won in the World

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Championships of 85 and buys a thousand boxes of donuts and graphs his weight [Randy surrounded by doughnut boxes]

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gain after each box he makes it through the whole batch and checks his results

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looks like he forgot to record his weight after 200 boxes and 600 boxes

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instead of doing his experiment all over again and buying another thousand donut

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boxes he decides to use something called limits to estimate his weight gain at

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those missing points here's what big Randy's graph currently looks like [Person points at missing data on graph]

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notice the missing points called holes at x equals 200 and the jump at x equals

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600 let's start by figuring out the hole at x equals 200 his weight gain at 200

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can be estimated by the Y value that corresponds to the graph when X is

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really really close to 200 which is called a limit at x equals 199 his

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weight gain was 49.8 pounds at x equals 301 his weight gain

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was 50.2 pounds it looks like the limit as X approaches

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200 boxes of donuts is about 50 pounds note that we did this even though the [Graph and young boy appears]

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graph is discontinuous and technically didn't have a value at that point we

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just guessed we can try to find the limit of a function at any x value [Woman teaching students about x value]

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here big Randy only cares about the limit of the graph at x equals 200 and

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600 boxes, now let's look at the jump at 600 boxes a limit requires that the Y

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values are the same going from x values greater than or less than the x value in

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question in this case 600 at 599.99

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boxes his weight gain was 98.9 pounds and at 600.01

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boxes his weight gain was a 110 pounds it might look like

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the weight gained at six hundred boxes could be a hundred to 105 or even 108

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pounds but the problem is there is such a small space between 599.99

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and 600.01 that there's only [Boy discussing weight gain]

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one space for a single value in other words the values at 599.99

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and 600.01 boxes need to be

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almost the same like at two hundred or the limit to exist

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so at 600 the limit does not exist well what does that mean it means that [Question marks appear by the graph]

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something wacky we must have happened at box 600 it's all coming back to him now

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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]

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sorry Randy.....

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