A MathWikiből

A lap korábbi változatát látod, amilyen Gaebor (vitalap | szerkesztései) 2019. december 2., 16:24-kor történt szerkesztése után volt.

Tartalomjegyzék

Sage

You can log in with your leibniz username and password.

You can use this, or install it on your own from here: http://www.sagemath.org/

Let Y be your year of birth, M the month, and D the day, create these variables.
How much is Y divided by D? Associate this value with the b variable.
Let r be the remainder of Y / M.
What's the difference r - b?

Is it true that the square root of the square of a number is the number itself?
1. Use bool to convert to logical value
2. Is it true for real numbers? Positive numbers? (assume)
Prove $(x - y)(x + y) = x 2 - y 2$
Prove $( - 1) 2 n = 1$ where n is integer!

Is 2018 a prime? (use the is_prime() function)
Were you born on a prime day? (use the D variable!)
Solve the equation Dx² + Mx − br = 0 using the solve(f, variable) function!
- x needs to be a symbolic variable!
- f can be a function, formula or an equation.
Solve the equation numerically! Use the find_root(f, min, max) function, where min and max defines an interval where Sage looks for the solution.
- this only works is you have one variable!
Solve the above equation symbolically (make D, M, b, r symbolic variables, then use solve)!
Differentiate the function Értelmezés sikertelen (ismeretlen függvény\cdotx): \sin(x)\cdot\cos(x)\cdotx^2

.

Integrate the previous function.
Calculate the limit of Értelmezés sikertelen (formai hiba): \lim_{n\to\infty}\right(1 + \frac3n\left)^{4n}

Let f be the following function: f(x,y) = (x+2*y)^3
Substitute 3 into x; then 4 into x and 2 into y. What's the result? ( use the subs() method of f)
Expand f! (expand())
Using the above, calculate the Taylor series of Értelmezés sikertelen (ismeretlen függvény\cdotx): \sin(x)\cdot\cos(x)\cdotx^2

up until the 4th member. (you can differentiate and integrate a function f by f.diff(x))

Plot a cosine curve from 0 to 4*pi!
Plot the $(x - 2) 2 + 3$ polynomial from -2 to 4, color it green!
Plot next to the previous one (using the show function) the function $x 3 - 3 * x + 6$ in red!
Plot a circle: cirlce((coordinates of the center), radius, optional). The "optional" can be: color, aspect_ratio=True so that the ratio of the x and y axis are kept, otherwise we might get an ellipse.