bxdin's profile - activity

I plotted the 2 following equations: (2x^3+2x) / (x^2+1) 2*x

p1 = plot((2*x^3+2*x) / (x^2+1), (x,-15,15), ymin=-15, ymax=15)
p2 = plot(2*x, (x,-15,15), ymin=-15, ymax=15, color='red') 
p0= p1+p2
show(p0)

And they both displayed the same output: I tried to do, (2x^3+2x) / (x^2+1) , but was displayed, 2*(x^3 + x)/(x^2 + 1)

How can I get 2*x to be displayed as the output?

I did .1/8, and the output was 0.0125000000. Is there a way to get it to display as 1/80.

Essentially, a question reads: Graph the polar curve r = 4cos(2?), where ? is a radian angle.

The graph of the curve looks like a 4 leafed clover.

The following function, r=3cos(?), looks like a circle centered at (3/2, 0).

I currently run Sage math 5.9 through, VirtualBox Fedora linux virtual machine, on Microsoft Windows 7.

I performed the following calculations.

eq1i = integral( sqrt( 1 + 1/(4*x))  )
f(x) = eq1i.subs(x=x)
show(eq1i)
float( f(4) - f(1) )

As you may see, I did show(eq1i), to display the integral result in a more readable format. I'd like to to take a screenshot of my results in Sage, so then I can use an image editing program in Windows, such as MS Paint or Adobe Photoshop, and crop out the result of show(eq1i), result.

According to the author, x=ln(y) should go through y=1, not x=1, making the plot look similar to a half U on the positive side of the x-axis, instead of a half C, on the the positive side of the y-axis.

var('y')
f=ln(y)
plot(f, (x,-5,5), ymin=-5, ymax= 5, aspect_ratio=1)

Awesome, thanks.

The following code is an example of plotting the equation: x = y^2-3x-5y+7, i.e. an equation solved for x:

var('y')
f = y^2-3*x-5*y+7
Yax = x
Xax = y
p1= implicit_plot(f, (x,-4, 4), (y,-2, 6))
p3= implicit_plot(Yax,  (x,-4, 4), (y,-2, 6),color='black')
p4= implicit_plot(Xax,  (x,-4, 4), (y,-2, 6),color='black')
p0= p1+p3+p4
show(p0)

According to the author, he solved the following equation in terms of x: x^2+y^2 = 25 He got the following: x = sqrt(25 - y^25) and x = -sqrt(25-y^2), i.e. ± sqrt(25 - y^25).

According to him, he plotted the 2 separate results to obtain a circle plot/graph.

How can I generate such an output on Sage 5.9?

The following was my best attempt, but I received no output for the plot of: sqrt(25-y^2):

var('y')
f = sqrt(25-y^2)
Yax = x
Xax = y
p1= implicit_plot(f, (x,-50, 50), (y,-50, 50))
p3= implicit_plot(Yax,  (x,-50, 50), (y,-50, 50), color='black')
p4= implicit_plot(Xax,  (x,-50, 50), (y,-50, 50), color='black')

p0= p1+p3+p4
show(p0)

The following is my syntax to generate the plot:

e1= x^3 + 4*x - 7
f(x)= e1.subs(x=x)
p1= plot(e1, (x,-15,15), ymin=-15, ymax=15)
p0= p1
show(p0)

Now to try and generate where on the x-axis the the plot crossed, 1.255 according to the author, I tried to get sage to solve for x, but it generated irrelevant answers:

ans = (solve(x^3 + 4*x - 7 == 0, x))
print (ans)
show(ans)

I tried substituting the value that didn't include imaginary into the original equation: x^3 + 4*x - 7, I got 1.333 x 10^-15, which is totally different from the author's.

The original question was: given f(x) = x^3 + 4*x - 2, one needs to evaluate f^-1(-5).