Calculus Formulas

• What does Limit mean?


  $L =$$\lim_{x\to\infty} f(x)$ if and only if for some positive number $\epsilon$, there is a positive number $\delta$that if x is within $\delta$units of c, f(x) is within $\epsilon$units of L.
• What is the Limit Sum Law?


  $\lim_{x\to a}((f(x)+$$g(x))=$$\lim_{x\to a}f(x)+$$\lim_{x\to a}g(x)$
• What is the Limit Difference Law?


  $\lim_{x\to a}(f(x)-g(x)) =$$\lim_{x \to a}f(x)-\lim_{x \to a}g(x)$
• What is the Constant Multiple Laws for Limits?


  $\lim_{x\to a}(cf(x)) =$$c\lim_{x\to a}f(x)$
• What is the Limit Product Law?


  $\lim_{x\to a}(f(x)*$$g(x)) =$$(\lim_{x\to a}f(x))*$$(\lim_{x\to a}g(x))$
• What is the Limit quotient Law?


  $\lim_{x\to a} (\frac{f(x)}{g(x)})=$$\frac{\lim_{x\to a}f(x)}{\lim_{x\to a}g(x)}$
• What is the Limit Power Law?


  $\lim_{x\to a}((f(x))^n)=$$(\lim_{x\to a}f(x))^n$