The Algebra of Limits

Calculate the following limit:

  • Answer:

You probably found this out by just plugging in the value 3, and that's okay. This was what you were supposed to do.

But what if we treat this fraction as a ratio of two functions? Let's say we have ,

Calculate these new limits:

  • Answer:

Hm. There seems to be a pattern here. The limit of seems to be equal to the limit of over the limit of . This is the first concept you have just learned about!

You can treat the limit of a function made up of a ratio, product, sum and difference of functions as a ratio, product, sum and difference of the limits of those functions.

Things get a bit more interesting when we introduce the next topic:
The Limits of Composite Functions

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