Bound Variable

These are variables that are temporary, not used directly in the statement. Commonly used as x in Set-Builder Notation like $x|x\in R$

Calculus

When you want to express another term in terms of $\delta$. You would usually assume the bound to then be 1,

Finding Bounds

In proving ${\lim }_{x\to c}f(x)=L$, $\delta$ when trying to bound $\delta <D$ for some constant $D$, and $f(x)$ has an asymptote at $x=x_0$ then $D=|c-x_0|$.

Examples

${\lim }_{x\to 1}\frac{1}{x^2-2}$

• $c=1$ (the x at the point of interest)
• $x_0=\sqrt{2}$ (the x at the asymptote) Then $D=|1-\sqrt{2}|=\sqrt{2}-1$