Math 161 Interactive Lecture Notes

This page contains lecture notes for Math 161, organized by section.

Preliminaries

$\mathbb{R}$
I
$(ab)^n = a^nb^n$
II
$A^2 - B^2$
III
$\dfrac{1}{x+1} - \dfrac{1}{x}$
IV

Chapter 1: Functions and Sequences

\(f(x)\)
1.1
\(\sin(x)\)
1.2
\(f\circ g\)
1.3
\(b^x\)
1.4
\(\ln x\)
1.5
\(a_n\)
1.6

Chapter 2: Limits

\(\displaystyle\lim_{n\rightarrow\infty}a_n\)
2.1
\(\displaystyle\lim_{x\rightarrow\infty}f(x)\)
2.2
\(\displaystyle\lim_{x\rightarrow a}f(x)\)
2.3
\(\displaystyle\lim_{x\rightarrow a}\left[f(x)g(x)\right]\)
2.4
\(\displaystyle\lim_{x\rightarrow a}f(x) = f(a)\)
2.5

Chapter 3: Derivatives

\(\displaystyle\lim_{h\rightarrow 0}\dfrac{f(a + h) - f(a)}{h}\)
4.1
\(\displaystyle\lim_{h\rightarrow 0}\dfrac{f(x + h) - f(x)}{h}\)
3.2
\(\displaystyle\dfrac{d}{dx}x^n = nx^{n-1}\)
3.3
\(\dfrac{d}{dx}\left[f(x)g(x)\right]\)
3.4
\(\dfrac{d}{dx}\left[\sqrt{xy}\right]\)
3.5
\(\dfrac{d}{dx}\ln x\)
3.7
\(f(a) + f'(a)(x - a)\)
3.8

Chapter 4: Applications of Derivatives

\(f'(x) = 0\)
4.1
\(f'(x) > 0\)
4.2
\(\displaystyle\lim_{x\rightarrow a}\dfrac{f'(x)}{g'(x)}\)
4.3
\(4.4\)
4.4