\item % section 2.3, extra 3. Can the following be the definition for $\lim_{x\to c} f(x) \neq L$? Explain. \begin{quote} For any $\delta >0$, there exists an $\epsilon_0 > 0$ and an $x_0 \in (c-\delta, c)\cup (c, c+\delta)$ such that $|f(x_0) - L | \geq \epsilon_0$. \end{quote} % Homework Assignment for Week 02 \item % One-sided limit % Section 2.4: Problems 26, 34, 42 Section 2.4: Problems 26, 34, 42, 48. \item % variants of (sin t)/t Chap 2: Problems 25 (Hint: $1-\cos x = 2 \sin^2 {x\over 2}$), 26 on page 121. \item % Continuity Section 2.5: problems 64, 67, 77 (Need not graph it). \item % Limits involving infinity Section 2.6: problems 92, 93, % 94, 100 (need not graph it, just find all horizontal, vertical and oblique asymptotes). \item % Section 2.6: Limits involving infinity Read Definition of the limits in p87, p104, p110 and p116. Then verify the following statements using formal definition of limits: \begin{description} \item[a.] % (a) is same as section 2.6: problem 94. $$ \lim_{x \to 0^+} {1\over x} = \infty $$ \item[b.] $$ \lim_{x \to \infty} -x^2 = -\infty $$ \end{description}