# Calculus with Functions II: MATH 232, Spring 2014

• Hello and welcome to Math 232!

• The keys to success in this class:
• Read the sections carefully before class
• Be ready and willing to participate during class
• Do all of the homework within one day after class
• Get help quickly when you need it
• No, seriously, read the list above and figure out how to make it happen.

$$\lim_{x \to c} f(x) = L \mbox{ if } \forall \epsilon>0, \exists \delta>0 \mid x \in (c-\delta,c+\delta) \Rightarrow f(x) \in (L-\epsilon,L+\epsilon)$$ $$f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$$ $$\int_a^b \!\!\!f(x) \; dx = \lim_{n \to \infty} \sum_{k=1}^{\infty} f(x_k^*) \; \Delta x, \mbox{ where } \Delta x = \tfrac{b-a}{n}, x_k = a+k\,\Delta x, x_k^* \in [x_{k-1},x_k]$$