Math 141 Interactive Lecture Notes

This page contains lecture notes for Math 141, organized by section.

Preliminaries

I

$(ab)^n = a^nb^n$

II

III

$\dfrac{1}{x+1} - \dfrac{1}{x}$

IV

V

Chapter 1: Limits

1.4

$\displaystyle\lim_{x\rightarrow a} f(x) = L$

1.5

$\displaystyle\lim_{x\rightarrow a} [f(x)g(x)]$

1.6

$\displaystyle\lim_{x\rightarrow a} f(x) = f(a)$

1.8

Chapter 2: Derivatives

\(\displaystyle\lim_{h\rightarrow 0}\dfrac{f(a + h) - f(a)}{h}\)

2.1

\(\displaystyle\lim_{h\rightarrow 0}\dfrac{f(x + h) - f(x)}{h}\)

2.2

\(\ \dfrac{d}{dx}[f(x)g(x)]\)

2.3

\(\ \dfrac{d}{dx}(\sin x) \)

2.4

\(\ \dfrac{d}{dx} f(g(x)) \)

2.5

\(\ \dfrac{d}{dx} [\sqrt{xy}] \)

2.6

\(\ \dfrac{d}{dt} \left[\dfrac{4}{3}\pi r^3\right] \ \)

2.8

Chapter 3: Applications of Differentiation

\(\ f'(c) = 0 \)

3.1

\(\ f'(c) = \dfrac{f(b) - f(a)}{b - a} \)

3.2

\(\ f'(c) > 0 \)

3.3

\(\ \displaystyle\lim_{x\rightarrow \infty}f(x) = L \)

3.4

3.9

Chapter 4: Integrals

\(\ \displaystyle \lim_{n\rightarrow\infty} \sum^n_{i = 1}f(x_i)\Delta x \)

4.1

\(\ \displaystyle\int^b_a f(x) \)

4.2

\(\displaystyle\dfrac{d}{dx}\int^x_a f(t) \ dt = f(x) \)

4.3