Difference between revisions of "Available Functions"
m (Undo revision 21833 by 188.236.193.7 (talk)  undo vandalism) Tag: Undo 

(32 intermediate revisions by 21 users not shown)  
Line 7:  Line 7:  
* ^ or ** You can use either ^ or ** for exponentiation, e.g. 3^2 or 3**2 
* ^ or ** You can use either ^ or ** for exponentiation, e.g. 3^2 or 3**2 

* Parentheses: ()  You can also use square brackets, [ ], and braces, { }, for grouping, e.g. [1+2]/[3(4+5)] 
* Parentheses: ()  You can also use square brackets, [ ], and braces, { }, for grouping, e.g. [1+2]/[3(4+5)] 

−  * Note: 1/2x is evaluated from 
+  * Note: 1/2x is evaluated from left to right and means <math>\frac{1}{2}x</math> which might not have been what you meant. 
+  √ 

+  +*k 

====Syntax for entering expressions==== 
====Syntax for entering expressions==== 

−  * Be careful entering expressions just as you would be careful entering expressions in a calculator. 

+  * '''Use the "Preview Button" to see exactly how your entry looks. E.g. to tell the difference between 1+2/3*4 and (1+2)/(3*4) click the "Preview Button".''' 

−  * '''Use the "Preview Button" to see exactly how your entry looks. E.g. to tell the difference between 1+2/3*4 and [1+2]/[3*4] click the "Preview Button".''' 

+  * Sometimes using the * symbol to indicate multiplication makes things easier to read. For example (1+2)*(3+4) and (1+2)(3+4) are both valid. So are 3*4 and 3 4 (3 space 4, not 34) but using a * makes things clearer. 

−  * Sometimes using the * symbol to indicate mutiplication makes things easier to read. For example (1+2)*(3+4) and (1+2)(3+4) are both valid. So are 3*4 and 3 4 (3 space 4, not 34) but using a * makes things clearer. 

* Use ('s and )'s to make your meaning clear. You can also use ['s and ]'s and {'s and }'s (except in contexts where those have special meanings, like creating intervals or sets). 
* Use ('s and )'s to make your meaning clear. You can also use ['s and ]'s and {'s and }'s (except in contexts where those have special meanings, like creating intervals or sets). 

* Don't enter 2/4+5 (which is 5.5) when you really want 2/(4+5) (which is 2/9). 
* Don't enter 2/4+5 (which is 5.5) when you really want 2/(4+5) (which is 2/9). 

* Don't enter 2/3*4 (which is 8/3) when you really want 2/(3*4) (which is 2/12). 
* Don't enter 2/3*4 (which is 8/3) when you really want 2/(3*4) (which is 2/12). 

* Entering big quotients with square brackets, e.g. [1+2+3+4]/[5+6+7+8], is a good practice. 
* Entering big quotients with square brackets, e.g. [1+2+3+4]/[5+6+7+8], is a good practice. 

−  * Be careful when entering functions. It's always good practice to use parentheses when entering functions. Write sin(t) instead of sint or sin t even though WeBWorK is smart enough to '''usually''' accept sin t or even sint. For example, sin 2t is interpreted as sin(2)t, i.e. (sin(2))*t so be careful. 
+  * Be careful when entering functions. It's always good practice to use parentheses when entering functions. Write sin(t) instead of sint or sin t even though WeBWorK is smart enough to '''usually''' accept sin t or even sint. For example, sin 2t is interpreted as sin(2)t, i.e. (sin(2))*t, so be careful. 
−  * You can enter sin^2(t) as a 
+  * You can enter sin^2(t) as a shortcut although mathematically speaking sin^2(t) is shorthand for (sin(t))^2 (the square of sin of t). (You can enter it as sin(t)^2 or even sint^2, but don't try such things unless you '''really''' understand the precedence of operations. The "sin" operation has highest precedence, so it is performed first, using the next token (i.e. t) as an argument. Then the result is squared.) You can always use the Preview button to see a typeset version of what you entered and check whether what you wrote was what you meant. :) 
* For example 2+3sin^2(4x) will work and is equivalent to 2+3(sin(4x))^2 or 2+3sin(4x)^2. Why does the last expression work? Because things in parentheses are always done first [ i.e. (4x)], next all functions, such as sin, are evaluated [giving sin(4x)], next all exponents are taken [giving sin(4x)^2], next all multiplications and divisions are performed in order from left to right [giving 3sin(4x)^2], and finally all additions and subtractions are performed [giving 2+3sin(4x)^2]. 
* For example 2+3sin^2(4x) will work and is equivalent to 2+3(sin(4x))^2 or 2+3sin(4x)^2. Why does the last expression work? Because things in parentheses are always done first [ i.e. (4x)], next all functions, such as sin, are evaluated [giving sin(4x)], next all exponents are taken [giving sin(4x)^2], next all multiplications and divisions are performed in order from left to right [giving 3sin(4x)^2], and finally all additions and subtractions are performed [giving 2+3sin(4x)^2]. 

* Is 5^2 positive or negative? It's negative. This is because the square operation is done before the negative sign is applied. Use (5)^2 if you want to square negative 5. 
* Is 5^2 positive or negative? It's negative. This is because the square operation is done before the negative sign is applied. Use (5)^2 if you want to square negative 5. 

Line 38:  Line 37:  
* 2.1E2 is the same as 210 
* 2.1E2 is the same as 210 

* 2.1E2 is the same as .021 
* 2.1E2 is the same as .021 

+  
+  ====Interval Notation==== 

+  
+  Some problems require you to enter an interval of real numbers. 

+  * (2,5) the open interval from 2 to 5, i.e. all real numbers greater than 2 and smaller than 5 

+  * [2,5) the halfopen interval containing all real numbers greater than or equal to 2 and smaller than 5 

+  * (inf, 10] all real numbers less than or equal to 10 (inf stands for infinity) 

====Mathematical Functions Available In WeBWorK==== 
====Mathematical Functions Available In WeBWorK==== 

Line 46:  Line 52:  
* sqrt(x)  The square root of x. Also can be written x^(1/2). 
* sqrt(x)  The square root of x. Also can be written x^(1/2). 

* abs(x)  The absolute value of x. Also can be written x. 
* abs(x)  The absolute value of x. Also can be written x. 

−  
−  '''In this site you will find more information about WebWorks more advanced features ''' [https://sites.google.com/view/mate3172uprb/p%C3%A1ginaprincipal please access this WebWork link.]. '''This page is cake of titi and in the search of the immortality of the crab.''' 

=====Exponential and Logarithmic Functions===== 
=====Exponential and Logarithmic Functions===== 

−  * exp(x)  The same function as e^x 

+  
−  * 
+  * ln(x)  The natural logarithm (logarithm to the base e) 
−  * 
+  * log10(x)  This is usually the natural log but your professor may have redefined this as log to the base 10 
−  +  log(y) 

=====Trigonometric Functions===== 
=====Trigonometric Functions===== 

Line 59:  Line 63:  
'''Note''': All of the trigonometric functions use '''radian''' measure. 
'''Note''': All of the trigonometric functions use '''radian''' measure. 

−  * cos(x) 

* sin(x) 
* sin(x) 

+  * cos(x) 

* tan(x) 
* tan(x) 

+  * cot(x) 

* sec(x) 
* sec(x) 

−  * cot(x) 

* csc(x) 
* csc(x) 

Line 91:  Line 95:  
=====Other Functions===== 
=====Other Functions===== 

−  * n!  n factorial (defined for nonnegative integers) 
+  * n!  n factorial (defined for nonnegative integers), can also be written as fact(n) 
* sgn(x)  the sign function, either 1 (if x < 0), 0 (if x = 0), or 1 (if x > 0) 
* sgn(x)  the sign function, either 1 (if x < 0), 0 (if x = 0), or 1 (if x > 0) 

Line 97:  Line 101:  
* step(x)  the step function (1 if x > 0, 0 otherwise.) 
* step(x)  the step function (1 if x > 0, 0 otherwise.) 

−  * fact(n)  another name for n!, 

* P(n,k) = n*(n1)*(n2)...(nk+1) the number of ordered sequences of k elements chosen from n elements 
* P(n,k) = n*(n1)*(n2)...(nk+1) the number of ordered sequences of k elements chosen from n elements 

Latest revision as of 15:02, 5 July 2021
Contents
Mathematical Symbols Available In WeBWorK
 + Addition
  Subtraction
 * Multiplication can also be indicated by a space or juxtaposition, e.g. 2x, 2 x or 2*x, also 2(3+4).
 / Division
 ^ or ** You can use either ^ or ** for exponentiation, e.g. 3^2 or 3**2
 Parentheses: ()  You can also use square brackets, [ ], and braces, { }, for grouping, e.g. [1+2]/[3(4+5)]
 Note: 1/2x is evaluated from left to right and means [math]\frac{1}{2}x[/math] which might not have been what you meant.
√ +*k
Syntax for entering expressions
 Use the "Preview Button" to see exactly how your entry looks. E.g. to tell the difference between 1+2/3*4 and (1+2)/(3*4) click the "Preview Button".
 Sometimes using the * symbol to indicate multiplication makes things easier to read. For example (1+2)*(3+4) and (1+2)(3+4) are both valid. So are 3*4 and 3 4 (3 space 4, not 34) but using a * makes things clearer.
 Use ('s and )'s to make your meaning clear. You can also use ['s and ]'s and {'s and }'s (except in contexts where those have special meanings, like creating intervals or sets).
 Don't enter 2/4+5 (which is 5.5) when you really want 2/(4+5) (which is 2/9).
 Don't enter 2/3*4 (which is 8/3) when you really want 2/(3*4) (which is 2/12).
 Entering big quotients with square brackets, e.g. [1+2+3+4]/[5+6+7+8], is a good practice.
 Be careful when entering functions. It's always good practice to use parentheses when entering functions. Write sin(t) instead of sint or sin t even though WeBWorK is smart enough to usually accept sin t or even sint. For example, sin 2t is interpreted as sin(2)t, i.e. (sin(2))*t, so be careful.
 You can enter sin^2(t) as a shortcut although mathematically speaking sin^2(t) is shorthand for (sin(t))^2 (the square of sin of t). (You can enter it as sin(t)^2 or even sint^2, but don't try such things unless you really understand the precedence of operations. The "sin" operation has highest precedence, so it is performed first, using the next token (i.e. t) as an argument. Then the result is squared.) You can always use the Preview button to see a typeset version of what you entered and check whether what you wrote was what you meant. :)
 For example 2+3sin^2(4x) will work and is equivalent to 2+3(sin(4x))^2 or 2+3sin(4x)^2. Why does the last expression work? Because things in parentheses are always done first [ i.e. (4x)], next all functions, such as sin, are evaluated [giving sin(4x)], next all exponents are taken [giving sin(4x)^2], next all multiplications and divisions are performed in order from left to right [giving 3sin(4x)^2], and finally all additions and subtractions are performed [giving 2+3sin(4x)^2].
 Is 5^2 positive or negative? It's negative. This is because the square operation is done before the negative sign is applied. Use (5)^2 if you want to square negative 5.
 When in doubt use parentheses!!! :)
 The complete rules for the precedence of operations, in addition to the above, are
 Additions and subtractions are performed left to right: 12+3 = (12)+3 = 2.
 Multiplications and divisions are performed left to right: 2/3*4 = (2/3)*4 = 8/3.
 Exponents are taken right to left: 2^3^4 = 2^(3^4) = 2^81 = a big number.
 Use the "Preview Button" to see exactly how your entry looks. E.g. to tell the difference between 1+2/3*4 and [1+2]/[3*4] click the "Preview Button".
Mathematical Constants Available In WeBWorK
 pi This gives 3.14159265358979, e.g. cos(pi) is 1
 e This gives 2.71828182845905, e.g. ln(e*2) is 1 + ln(2)
Scientific Notation Available In WeBWorK
 2.1E2 is the same as 210
 2.1E2 is the same as .021
Interval Notation
Some problems require you to enter an interval of real numbers.
 (2,5) the open interval from 2 to 5, i.e. all real numbers greater than 2 and smaller than 5
 [2,5) the halfopen interval containing all real numbers greater than or equal to 2 and smaller than 5
 (inf, 10] all real numbers less than or equal to 10 (inf stands for infinity)
Mathematical Functions Available In WeBWorK
Unless otherwise specified, all of the functions listed below are enabled by default. However, sometimes one or more of these functions is disabled for a particular WeBWorK problem because the instructor wants you to calculate the answer by some means other than just using the function.
 sqrt(x)  The square root of x. Also can be written x^(1/2).
 abs(x)  The absolute value of x. Also can be written x.
Exponential and Logarithmic Functions
 ln(x)  The natural logarithm (logarithm to the base e)
 log10(x)  This is usually the natural log but your professor may have redefined this as log to the base 10
log(y)
Trigonometric Functions
Note: All of the trigonometric functions use radian measure.
 sin(x)
 cos(x)
 tan(x)
 cot(x)
 sec(x)
 csc(x)
 arcsin(x), asin(x), or sin^1(x)
 arccos(x), acos(x), or cos^1(x)
 arctan(x), atan(x), or tan^1(x)
 arccot(x), acot(x), or cot^1(x)
 arcsec(x), asec(x), or sec^1(x)
 arccsc(x), acsc(x), or csc^1(x)
Hyperbolic Trig Functions
 sinh(x)
 cosh(x)
 tanh(x)
 sech(x)
 csch(x)
 coth(x)
 arcsinh(x), asinh(x), or sinh^1(x)
 arccosh(x), acosh(x), or cosh^1(x)
 arctanh(x), atanh(x), or tanh^1(x)
 arcsech(x), asech(x), or sech^1(x)
 arccsch(x), acsch(x), or csch^1(x)
 arccoth(x), acoth(x), or coth^1(x)
Other Functions
 n!  n factorial (defined for nonnegative integers), can also be written as fact(n)
 sgn(x)  the sign function, either 1 (if x < 0), 0 (if x = 0), or 1 (if x > 0)
These functions are available for some problems, but may not be enabled for others (for authoring information see step functions):
 step(x)  the step function (1 if x > 0, 0 otherwise.)
 P(n,k) = n*(n1)*(n2)...(nk+1) the number of ordered sequences of k elements chosen from n elements
The following functions are not enabled in student answers by default:
 C(n,k) = "n choose k" the number of unordered sets of k elements chosen from n elements
 ceil(x) The ceiling function that rounds up to the nearest integer
 floor(x) The floor function that rounds down to the nearest integer
 max(x,y) The max function
 min(x,y) The min function
These can be used in authoring problems if PGauxiliaryFunctions.pl
is included in the problem. In order to use P(n,k) and C(n,k), you must be in the IntegerFunctions context.