Is a semi-circle a function? In this graph of a semi-circle, the vertical line meets only at one point. Consider the function \[f(x) = 2^ for bottom semi-circle.
b is normally a number greater than 1 (although it need only be greater than 0 and not equal to 1). T HE LOGARITHMIC FUNCTION WITH BASE b is the function. Figure A Logarithmic Functions and Graphs Definition of Logarithmic Function: The logarithmic. has the set of positive real numbers as its range. has the set of real numbers as its domain. To indicate the limits of evaluation, either bracket them after the expression you're evaluating, or else spell out "evaluated between (this) and (that)".Properties of an exponential function: For all positive real numbers, the 1. To indicate a partial derivative, just spell out "partial". Follow this with the limits of integration (if any), the integrand, and the differential. The "int" abbreviation for "integral" is fairly standard. Follow this with brackets showing what is heading toward what, and then put the argument. The "lim" abbreviation for "limit" is standard. Whatever notation you use for a summation, be sure to define what you mean by restating the first summation in words. If you use the absolute-value-bar notation for the determinant, state what you mean. Use bars (the "pipe" character, shown as a (possibly broken) line on your keyboard, somewhere above the "Enter" key) to delineate the rows. Be sure to say what you mean by this, and try to use "CODE" or "PRE" tags or a fixed-width font.ĭeterminants are also hard to format with only text. The bracket design, using outer brackets for the matrix and inner brackets for the rows, has arisen from graphing-calculator notation. Matrices are just about impossible to format with text. Write the transpose or inverse of a matrix using superscript notation. Don't worry about the arrows over the tops of some vectors. Instead, either spell out "cross" or else (on a PC) hold down the "ALT" key and type "0215" on the numeric keypad, using generous spacing so your meaning is clear. As long as you've specified that the context is vectors, you can ignore the arrows.ĭon't use the letter "X" between the vectors, as this will be confused as being a third vector. You can use the "less than" and "greater than" signs for vectors.Īs long as you define the asterisk to mean the dot product, you can use this for dotting two vectors. If you use it, define it first, so they know you mean what is shown in the first line. Not everybody is familiar with the "cis" notation.
You don't have define what e is in your post. The natural exponential e is a commonly-known value, just like pi. When writing complex numbers, just use the " i" as usual. It's " pi", not " pye" or " pie".) You may find it helpful to use parentheses, as in " sin". Otherwise, spell out the name, or replace "beta" in your exercise with a Latin letter.ĭo not use " m" or " n" to stand for " π", since m and n are variables and π is a number. You can (on a PC) insert a character similar to "beta" by holding down the "ALT" key and typing "0223" on the numeric keypad. Otherwise, spell it out, or pick a Latin letter, such as "t". To indicate "degrees", either write the word out use an asterisk and explain what it means or else (on a PC), hold down the "ALT" key and type "0176" to insert the character long as you define yourself, it's okay to use for "theta". Use parentheses to make clear that you mean "sine of 2 x", not "the square of the sine of x". Use parentheses to clearly delineate what goes where. If you're squaring the argument, put the power on the argument. If you're squaring the sine, put the power on the sine.
Put parentheses around the argument of any function, including sine and cosine.
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