Continuity

Proving at point c

• $f(c)$ exists
• ${\lim }_{x\to c}f(x)$ exists
• ${\lim }_{x\to c}f(x)=f(c)$

Squeeze Theorem

If $g(x)\le f(x)\le h(x)$ (on an interval that contains c)

and ${\lim }_{x\to c}g(x)={\lim }_{x\to c}h(x)=L$ and they are all continuous on that interval

then ${\lim }_{x\to c}f(x)=L$

Intermediate Value Theorem

If $f(x)$ is continuous over the interval $[a,b]$

and $w$ is a value between $f(a)$ and $f(b)$

then there exists a value $c$ between $[a,b]$ such that $f(c)=w$

Limits to Infinity

• BOB0: Bigger on bottom → 0
• BOTN: Bigger on top → none
• EATS DC: Exponents are the same → Divide Coefficients