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konichiwa2x

HOW TO LATEX

The LaTeX typesetting system is a very useful tool helpful in typing mathematical formulas such as

which can otherwise be a very tedious process.

To type in latex, all you need to learn is a few simple codes and you are on your way!

Every symbol/mathematical term has a particular code associated with it. Once you learn the codes, just type them in the box provided in the following link:

TEXER and click "submit". Immediately, the 'latex' image will be generated below the "submit" button. Copy it and paste it in the goiit forums!

If you'd like to see how other members typed their math formulas, just hover the mouse above their latex images. It is a great way to learn from others!

Elementary Algebra:

1.1 Exponents and Subscripts

LaTeX employs the caret ^ symbol for exponents and the underscore _ symbol for subscripts.

x^8+3x^6+x^2+1=0 gives

.

If an exponent or subscript contains more than one character (e.g., 10, 80, or xy), then it must be surrounded by curly braces. For example:

a^{1/5}b^{10}c^{15} \leq100 gives $a^{1/5}b^{10}c^{15}leq100$ .

log_{10}{x} \geq 2 gives $log_{10}xgeq2$

By the way, \\ starts a new line, includes a space.

1.2 Roots/Radicals

To create square roots:

d=\sqrt{x^2+y^2} gives $d=sqrt{x^2+y^2}$

To generate cube roots, fourth roots, and so on, sqrt also accepts an optional argument enclosed in square brackets:

\sqrt[3]{8}+\sqrt[4]{16}=4 gives sqrt[3]{8}+sqrt[4]{16}=4

Curly braces are optional, so long as the argument consists of exactly one character.

1.3 Fractions

Here's how to produce nice-looking fractions:

\frac{1}{2}+ \frac{2}{3}= \frac{5}{6} gives rac{1}{2}+rac{2}{3}=rac{5}{6}

Put whatever you want in between the curly braces. Whatever you type will become the numerator and denominator.

Similarly, x= \frac{-b \pm \sqrt{b^2-4ac}}{2a} gives $x= rac{-bpmsqrt{b^2-4ac}}{2a}$

Trigonometry

Here are some commands that generate the names of common functions (sine and cosine, for example), as well as the notation used to name and measure lines and angles.

Many times Greek letters are used to denote angles or variables. For example, the commands corresponding to the Greek letters alpha, beta, gamma, pi, and theta are alpha, beta, gamma, pi, and heta respectively:

Names of many well-known functions (e.g., sin and cos), can be written in a non-italic font. For example:

cos{x},sin{x},sec{x}, an{x},cot{x}, an^{-1}{x},sin{-1}{x}. gives

\sin(\alpha+\beta)= \sin\alpha\cos\theta + \cos\alpha\sin\theta gives sin(alpha+eta)= sinalphacoseta + cosalphasineta

\cos\theta= \pm \sqrt{ \frac{1+cos(2\theta)}{2}} gives

\sin{\left( \frac{\pi}{2}-x\right)}= \cos x gives

Calculus

3.1 Limits

Limits are generated with lim. An underscore puts something under the lim:

lim_{x\to0} \frac{\sin x}{x}=1 gives $lim_{x o0} rac{sin x}{x}=1$

lim_{x\to5}\frac{x^2-10x+25}{x^2-7x+10}=0 gives

$lim_{x o5} rac{x^2-10x+25}{x^2-7x+10}=0$

3.2 Derivatives

Higher order derivatives. What you see there are single right quotes:

f(x)=x^3, f'(x)=3x^2, f''(x)=6x, f'''(x)=6 gives us f(x)=x^3, f

y=ln{x}\Longrightarrow \frac{dy}{dx}= \frac{1}{x} gives us

f'(a)= lim_{x\to a} \frac{f(x)-f(a)}{x-a} gives

3.3 Summations

Summations are generated with the sum command. Underscores and carets mark the lower and upper bounds respectively

\sum_{k=1}^{n}k= \frac{n(n+1)}{2} gives $sum_{k=1}^{n}k= rac{n(n+1)}{2}$

\sum_{k=0}^{\infty}r^k= \frac{1}{1-r} gives $sum_{k=0}^{infty}r^k= rac{1}{1-r}$

\pi = \sum_{k=0}^{infty} \frac{1}{16^k} \left( \frac{4}{8k+1}- \frac{2}{8x+4} - \frac{1}{8k+5}- \frac{1}{8k+6} \right) gives $pi = sum_{k=0}^{infty} rac{1}{16^k} left( rac{4}{8k+1}- rac{2}{8x+4} - rac{1}{8k+5}- rac{1}{8k+6} ight)$

\prod_{i=1}^{n} a_{i} gives $prod_{i=1}^{n} a_{i}$

3.4 Integrals

Create integrals with int:

\int ln x,dx=xln x-x+C gives intln x,dx=xln x-x+C

For definite integrals with limits,

\int_a^b x^2,dx= \frac{b^3}{3}- \frac{a^3}{3} gives $int_a^b x^2,dx= rac{b^3}{3}- rac{a^3}{3}$

For further symbols, visit the following link:

http://www.artofproblemsolving.com/LaTeX/AoPS_L_GuideSym.php

For convenience sake, and to reduce complexity, I have not included the code for vectors, determinants and matrices. If you require the code for these or need assistance, do nudge me.

All the best!!

Konichiwa2x

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