# Limit laws

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##### Intros
###### Lessons
1. Limit Laws Overview:
7 Properties of Limit Laws
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##### Examples
###### Lessons
1. Evaluating Limits of Functions
Evaluate the following limits using the property of limits:
1. $\lim_{x \to 2} x^2+4x+3$
2. $\lim_{x \to 2} 3(x^2+4x+3)^2$
3. $\lim_{x \to 1} \frac{2-3x+4x^2}{2+x^4}$
4. $\lim_{x \to 0} 4(3)^x$
5. $\lim_{x \to \frac{\pi}{2}} 3(\sin x)^4$
2. Evaluating Limits with specific limits given
Given that $\lim_{x \to 5} f(x)=-3$, $\lim_{x \to 5} g(x)=5$, $\lim_{x \to 5} h(x)=2$, use the limit properties to compute the following limits:
1. $\lim_{x \to 5} [5f(x)-2g(x)]$
2. $\lim_{x \to 5} [g(x)f(x)+3h(x)]$
3. $\lim_{x \to 5} \frac{2g(x)}{h(x)}$
4. $\lim_{x \to 5} \frac{5[f(x)]^3}{g(x)}$
###### Topic Notes
Here are some properties of limits:

1) $\lim_{x \to a} x = a$
2) $\lim_{x \to a} c = c$
3) $\lim_{x \to a} [cf(x)] = c\lim_{x \to a}f(x)$
4) $\lim_{x \to a} [f(x) \pm g(x)] = \lim_{x \to a}f(x) \pm \lim_{x \to a}g(x)$
5) $\lim_{x \to a} [f(x) g(x)] = \lim_{x \to a}f(x) \lim_{x \to a}g(x)$
6) $\lim_{x \to a} \frac{f(x)}{g(x)} = \frac{\lim_{x \to a}f(x)}{\lim_{x \to a}g(x)}$, only if $\lim_{x \to a}g(x) \neq0$
7) $\lim_{x \to a} [f(x)]^n=[\lim_{x \to a}f(x)]^n$

Where c is a constant, $\lim_{x \to a} f(x)$ and $\lim_{x \to a} g(x)$ exist.

Here is a fact that may be useful to you.
If $P(x)$ is a polynomial, then
$\lim_{x \to a} P(x)=P(a)$