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====Syntax for entering expressions====
 
====Syntax for entering expressions====
   
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* '''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".'''
 
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* Be careful entering expressions just as you would be careful entering expressions in a calculator.
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* 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.
 
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* '''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".'''
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* 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).
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* 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.
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* 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. :-)
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* You can enter sin^2(t) as a short cut 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.

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