1. Give the ϵ − δ definition of lim_{x→a} f(x) = l.

2. Use ϵ − δ definition to prove the following : if lim_{x→a} f(x) = l, lim_{x→a} g(x) = m then lim_{x→a} f(x) + g(x) = l + m

3. State the Sandwich Theorem. (i.e. Squeezing Theorem )

4. Give the definition of ”f is continuous at a”.

5. f(x)=\{ \begin{matrix}x^{2} + 2 x < 1 \\ \frac{1}{x+1} x > 1 \end{matrix} .

Write down (1) lim_{x→1^{−}} f(x),

(2) lim_{x→1^{+}} f(x), (3) lim_{x→1} f(x) .