Inhaltsverzeichnis
- Enter: evaluate input
- Ctrl+Enter: check input but do no evaluate input, e.g. b+b stays b+b. Note that assignments are always evaluated, e.g. a := 5
- In an empty row type
- space bar for previous output
- ) for previous output in parentheses
- = for previous input
- Suppress output with a semicolon at the end of your input, e.g. a := 5;
Static row references insert text from another row, so your input is changed.
- # inserts the previous output
- #5 inserts the the output of row 5
- ## inserts the previous input
- #5# inserts the input of row 5
Dynamic row references use text from another row, but don't change your input.
- $ inserts the previous output
- $5 inserts the the output of row 5
- $$ inserts the previous input
- $5$ inserts the input of row 5
Toolbar
- Clicking a button in the toolbar applies a command to the currently edited row
- You can select part of the input text to only apply the operation to this selected part
- Assignments use the := notation, e.g. b := 5, a(n) := 2n + 3
- Variables and functions are always shared between the CAS view and GeoGebra if possible. If you define b:=5 in the CAS view, then you can use b in all of GeoGebra. If you have a function f(x)=x^2 in GeoGebra, you can also use this function in the CAS view.
- Simplify[ exp ] groups powers within terms, and then groups similar terms.
- Simplify[ 3a + 2a ] returns 5*a
Problem: `(2+2/3)*5`
Auswertung von 2+2 möglich (? Warnung ?)
- Delete(var)
- Leerdefinition? a:=
- Prozent verus Kanalgitter
- Numeric[ exp ], Numeric[ exp, precision ] tries to determine a numerical approximation of the given expression
- N[ 1/2 ] returns 0.5
- N[ sin(1), 20 ] returns 0.84147098480789650665250417564626038175641085
- Expand[ exp ]expands the given expression
- Expand[ (x-2) (x+3) ] returns x^2 + x - 6
- Factor[ exp ] factors the given expression
- Factor[ 2x^3 + 3x^2 - 1 ] returns 2*(x+1)^2 * (x-1/2)
- Solve2[equation1, equation2] solves two equations for x and y
- Solve2[x + y = 2, y = x] returns 1_1
- Solve2[equation1, equation2, var1, var2] solves two equations for var1 and var2
- Solve2[a + b = 2, a = b, a, b] returns 1_1
- Equations are written using the simple Equals sign, e.g. 3x + 5 = 7
- You can perform arithmetic operations on equations, e.g. (3x + 5 = 7) - 5 subtracts 5 from both sides of the equation. This is useful for manual equation solving.
You can use the Solve toolbar button or Solve command to solve equations.
- Solve[ equation ] solves an equation for x
- Solve[ x^2 = 4 ] returns {2, -2}
- Solve[ equation, var ] solves an equation for the given variable.
- o Solve[ 3a = 5b, a ] returns {5b / 3}
Solve nach x und y liefert eine Liste - ist nicht günstig (besser: Solutions)
Wenn nach Umformung substituiert wird, ergibt sich ein Fehler.
#1 - 4*(#2) Vereinfachen führt zu
(4 x + 5 y = 7)-4*((x - 2 y = -8)), Sorry, something went wrong. Please check your input.
Bem.: Hier sollte
- Vereinfacht werden
- keine doppelte Klammer kommen
- Die Eingabe
#1 -4*(#2)noch irgendwo zu sehen sein
- Adding equations, e.g. first row: 3x+6y=7, second row: x-y=2, then you can use $1 +6 $2 to add the two equations ($1, $2 are dynamic references to the first and second row). If you also want to draw the equations, you can label them, e.g. first row a: 3x+6y=7, second row b: x-y=2, then add them in the third row using a + 6b
- Solve and Solutions: Solve[x^2=4] returns {x=-2, x=2} while Solutions[x^2=4] returns {-2,2}
- For convenience, the following input is automatically rewritten:
- a:= is rewritten as Delete[a] and deletes/unbinds variable a
- 2+2= is rewritten as 2+2 by removing the trailing =
- f(x)=x^2 is rewritten as f(x):=x^2
- Note that a=3 is no longer rewritten as a:=3 to allow equations of this form too.
- Limit[ exp, var, value ], Limit[ exp, var, value, direction ] tries to determine the limit of an expression.
- Limit[ sin(x)/x, x, 0 ] returns 1
- Limit[ 1/x, x, 0, Left ] returns -Infinity
- Sum[ exp, var, from, to ] finds the sum of a sequence
- Sum[i^2, i, 1, 3] returns 14
- Sum[r^i, i,0,n] returns (1-r^(n+1))/(1-r)
- Sum[(1/3)^i, i,0,Infinity] returns 3/2
- Derivative[ function ], Derivative[ function, var ], Derivative[ function, var, n ] takes the derivative of a function with respect to the given variable. If no variable is given, „x“ is used.
- Derivative[ sin(x)/x^2, x ] returns (x^2*cos(x) - sin(x)*2*x) / x^4
- Derivative[ sin(a*x), x, 2 ] returns -sin(a*x)*a^2
- Integral[ function, var ], Integral[ function, var, x1, x2 ] finds the (definite) integral of a function with respect to the given variable
- Integral[ cos(x), x ] returns sin(x)
- Integral[ cos(x), x, a, b ] returns sin(b) - sin(a)
The following commands are symbolic equivalents to existing numeric GeoGebra commands, or they are direct mappings to MathPiper commands.
- GCD[ number, number ] gives the greatest common divisor of two numbers
- LCM[ number, number ] gives the least common multiple of two numbers
Editierhilfe
