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We give basic laws for working with limits.

In this section, we present a handful of rules called the Limit Laws that allow us to find limits of various combinations of functions.
True or false: If $f$ and $g$ are continuous functions on an interval $I$, then $f\pm g$ is continuous on $I$.
True False
True or false: If $f$ and $g$ are continuous functions on an interval $I$, then $f/g$ is continuous on $I$.
True False

We can generalize the example above to get the following theorems.

Where is $f(x) = \frac {x^2-3x+2}{x-2}$ continuous?
for all real numbers at $x=2$ for all real numbers, except $x=2$ impossible to say

Back in Theorem theorem:continuity we mentioned a big list of functions that were continuous. We mention them again in the following statement. We will study some of these functions in more detail in later sections. For now, we focus only on the fact that they are continuous.

Now, we give basic rules for how limits interact with composition of functions.

Because the limit of a continuous function is the same as the function value, we can now pass limits inside continuous functions.

Many of the Limit Laws and theorems about continuity in this section might seem like they should be obvious. You may be wondering why we spent an entire section on these theorems. The answer is that these theorems will tell you exactly when it is easy to find the value of a limit, and exactly what to do in those cases.

The most important thing to learn from this section is whether the limit laws can be applied for a certain problem, and when we need to do something more interesting. We will begin discussing those more interesting cases in the next section. For now, we end this section with a question:

### A list of questions

Let’s try this out.

Can this limit be directly computed by limit laws?
yes no
Compute:
Can this limit be directly computed by limit laws?
yes no
Can this limit be directly computed by limit laws?
yes no
Can this limit be directly computed by limit laws?
yes no
Can this limit be directly computed by limit laws?
yes no
Compute:
Can this limit be directly computed by limit laws?
yes no
Can this limit be directly computed by limit laws?
yes no
Can this limit be directly computed by limit laws?
yes no
Compute:
Can this limit be directly computed by limit laws?
yes no