# Limit laws

#### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

#### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

#### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

##### Intros
###### Lessons
1. Limit Laws Overview:
7 Properties of Limit Laws
##### 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
$\lim_{x \to a} P(x)=P(a)$