Limit Theorem Shown in Class

Note to start: $\sqrt{x^2}=x$ only sometimes

**In this class, $\infty$ is a symbol saying “Some unbounded process is going on.”

So, $\infty$ is not a number, and therefore writing $\frac{1}{\infty }$ is not allowed.

Limit theorem shown in class

For functions f(x) and g(x)

if ${\lim }_{x\to a}f(x)=k$, a real number, and if ${\lim }_{x\to a}g(x)=\pm \infty$,

Then, the limit ${\lim }_{x\to a}\frac{f(x)}{g(x)}=0$

Example: ${\lim }_{x\to \infty }\frac{4\to 4}{a\to \infty }=0$, by the Limit Theorem Shown in class OR draw an arrow from each value and show the value they approach.

Example: ${\lim }_{x\to \infty }\frac{5x+2}{x^2}={\lim }_{x\to \infty }\frac{x(5+\frac{2}{x})}{x\ast x}$