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