SELECTED EXAMPLES MARCH 4, 1998

GEORGE MCNULTY

Here is gather

∫_{0}^{∞} e^{x} dx = ∞ (1)

e^{iπ} = −1 (2) e^{2iπ} = 1 (3) π ≈ 3.14159 (4)

Here is align

(5) ∫_{0}^{∞} e^{x} dx = ∞^{(6)  e^{iπ} = −1}^{(7)  e^{2iπ} = 1}^{(8)  π ≈ 3.14159}^{(9)  ∫_{0}^{∞}e^{x} dx = ∞}

SELECTED EXAMPLES  MARCH 4, 1998  3

Here is multline

(10) ∫_{0}^{∞} e^{x} dx = ∞

e^{iπ} = −\frac{12345678}{12345678}

e^{2iπ} = 1

π ≈ 3.14159

Here is split inside gather

\begin{aligned}∫_{0}^{∞} e^{x} dx & = ∞ \\ e^{iπ} & = −\frac{12345678}{12345678} \end{aligned} (11)

e^{2iπ} = \frac{123}{123}

π ≈ 3.14159 (12) The integral sign (∫) is obtained with \int.

Here is gather*

∫_{0}^{∞} e^{x} dx = ∞

e^{iπ} = −1 e^{2iπ} = 1 π ≈ 3.14159

Here is align*

∫_{0}^{∞} e^{x} dx = ∞
e^{iπ} = −1
e^{2iπ} = 1
π ≈ 3.14159

SELECTED EXAMPLES  MARCH 4, 1998  5

Here is multline* ∫_{0}^{∞} e^{x} dx = ∞

e^{iπ} = −\frac{12345678}{12345678}

e^{2iπ} = 1

π ≈ 3.14159

Here is split inside gather*

\begin{aligned}∫_{0}^{∞} e^{x} dx & = ∞ \\ e^{iπ} & = −\frac{12345678}{12345678} \end{aligned}

e^{2iπ} = \frac{123}{123}

π ≈ 3.14159

Here is alignat

(13) ∫_{0}^{∞} e^{x} dx = ∞ e^{iπ} = −1
(14)  e^{2iπ} = 1  π ≈ 3.14159
(15)  ∫_{0}^{∞} e^{x} dx = ∞e^{iπ} = −1
(16)  e^{2iπ} = 1 π ≈ 3.14159

Here is xalignat

(17) ∫_{0}^{∞} e^{x} dx = ∞  e^{iπ} = −1
(18)  e^{2iπ} = 1  π ≈ 3.14159

(π) ∫_{0}^{∞} e^{x} dx = ∞  e^{iπ} = −1
e^{2iπ} = 1  π ≈ 3.14159

1 + 1 = 2 1 + 2 = 3 3 = 1 + 2 and \begin{aligned}a + b & = c \\ a + c & = d \\ 3 & = 1 + 2 \end{aligned}

x + y + some more stuff = something else

Definition of a function by cases

f(x) = \begin{cases}0 & if Ralph is awake \\ 1^{does it matter} & if Ralph is asleep \end{cases}

And, to conclude, some mathematical operators: Is sin(x) the same as sin(x)? Is logx the same as log x? Note the difference between lim_{n→∞}(1+1/n)^{n} = e and

lim_{n→∞}(1 + 1/n)^{n} = e.