$$ \begin{array}{1} \begin{array}{1} \text { The Sandwich Theorem } W \text { suppose that ) g(x) \leq f(x) \leq h(x) \text { for all } x \text { in some open interval containing cexcept possibly } W \text { at } x=C \text { itself. Suppose also that} \qquad \lim _{x ightarrow \infty) g(x)=\lim _{x ightarrow \infty) h(x)=L \text { Then } \lim _{x ightarrow \infty) f(x)=L \end{array} \text { 3. Show that } \lim _{x ightarrow 0) x^{2} \cos \left(x+\frac{1} {x^{3}} ight)=0 \end{array} $$ CS.JG. 120