Here is an arithmetic problem, 660 * 310.
I'm going give this exercise to Bart. So, the product of 660 and 310 is
204,600. But, what if I perturb these inputs a
little bit? Instead of assigning this multiplication
exercise, I could have assigned this multiplication exercise,
664 * 311. Let's give this to somebody else.
Hi. My name is Vadranna.
So, 664 * 311 is 206,504. Which isn't so far off of the answer that
Bart got when he multiplied 660 times 310 and got 204,600.
So, look at this. We've got two different problems.
The input to these multiplication problems are similar,
the outputs are also similar. Let's do some more, very similar
multiplication problems. [SOUND] Hello, my name is Sean Gory.
[SOUND] Oh, this is great. Look.
204,600, 206,504, 206,926, 204,702. We multiplied all of these pairs of
nearby numbers, and the result of the multiplications were also nearby.
There's a limit lesson hiding at all of this.
If the limit of f of x as x approaches a is L, and the limit of g of x as x
approaches a is M, then the limit of f of x times g of x as x approaches a is equal
to L times M. In other words, the limit of a product is
the product of the limits provided those limits exist [SOUND]