Math327

Basic Properties Of Limits

Triangle Inequality: {$ \abs{x+y} \leq \abs{x} \abs{y} $}. Keep in mind that this formula generalizes for any number of variables. this can be proven by induction for the skeptical.

unnamed inequality: {$ \abs{\abs{x} - \abs{y}} \leq \abs{x-y} $}.

we get tricks here.

Suppose {$\lim{a_n} = K$}
{$\lim{b_n} = L$}

then: 

       {$\lim{a_n + b_n} = L+K$}
        {$\lim{a_n - b_n} = L-K$}
        {$\lim{a_n \dot b_n} = LK$}
        {$\lim{\frac{a_n}{b_n}} = \frac{L}{K}$}