Matematika 1

113 days ago by Jure

plot.options 
       
{'fillalpha': 0.5, 'detect_poles': False, 'plot_points': 200,
'thickness': 1, 'alpha': 1, 'adaptive_tolerance': 0.01, 'fillcolor':
'automatic', 'adaptive_recursion': 5, 'aspect_ratio': 'automatic',
'exclude': None, 'legend_label': None, 'rgbcolor': (0, 0, 1), 'fill':
False}
{'fillalpha': 0.5, 'detect_poles': False, 'plot_points': 200, 'thickness': 1, 'alpha': 1, 'adaptive_tolerance': 0.01, 'fillcolor': 'automatic', 'adaptive_recursion': 5, 'aspect_ratio': 'automatic', 'exclude': None, 'legend_label': None, 'rgbcolor': (0, 0, 1), 'fill': False}
f(x)=x^2/(x^2+1) plot(f, (x,-10,10)) 
       
f(x)=3*x^2 g(x)=x*sin(x) a=plot(f, (x,-10,10)) b=plot(g, (x,-10,10),thickness=4.0,rgbcolor=(0.5,1,0),legend_label='x*sin(x)') show(a+b) 
       
fvar('x, y') graf3d= plot3d(y^2*x+3,(x,-3,3),(y,-3,3)) show(graf3d) 
       
f=(x+2)*(x-4)-(x+3)^2+4 g=2*x-1 result=solve(f==g,x) show(result[0]) p1=plot(f,(x,-5,5),color='red') p2=plot(g,(x,-5,5)) show(p1+p2) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}x = \left(-\frac{6}{5}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}x = \left(-\frac{6}{5}\right)
f=4^(x-1)-5 show(solve(f==0,x)) p3=plot(f,(x,-5,5)) show(p3) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \frac{\log\left(4\right) + \log\left(5\right)}{\log\left(4\right)}\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \frac{\log\left(4\right) + \log\left(5\right)}{\log\left(4\right)}\right]
j=(x-1)*(x+2)-x*(x+3) show(solve(j<=2,x)) plot(j,(x,-5,5)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x \geq \left(-2\right)\right]\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x \geq \left(-2\right)\right]\right]
var('y') show(solve([3*x-5*y==-2,2*x+4*y==6],x,y)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x = 1, y = 1\right]\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x = 1, y = 1\right]\right]
var('y') l=(x^2-3)/(x^2-2*x+1) p1=plot(l,(x,-5,5),) p1.ymax(5) p1.ymin(-5) p1.axes_labels([x,y]) show(p1) show(solve(l==0,x)) print(solve(x^2-2*x+1,x)) 
       

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\sqrt{3}, x = \sqrt{3}\right]
[ x == 1 ]

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\sqrt{3}, x = \sqrt{3}\right]
[ x == 1 ]
 
       
var ('n') def Sum(n): var ('a') rezultat=0 a=1 for a in range (1,n+1): rezultat=rezultat+a if rezultat != (a*(a+1))/2: return ("ne") a=a+1 return ("da") n=50 S=Sum(n) print(S) 
       
da
da
f=(x^2)/(x-1) a=plot(f,(x,-5,5)) a.ymax(5) a.ymin(-5) show(a) solve(f==0,x) 
       

[x == 0]

[x == 0]
f=(1/(x-2))+(1/(x+2)) a=plot(f,(x,-5,5)) a.ymax(5) a.ymin(-5) show(a) 
       
f=-(x+1)/(x+2) a=plot(f,(x,-5,5)) a.ymax(5) a.ymin(-5) show(a) 
       
f=x^3-x^2-x+1 k=-1/3 a=plot(f,(x,-20,20)) a.ymax(120) a.ymin(-120) show(a) show(solve(f==0,x)) show(f(-1/3)) 
       

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-1\right), x = 1\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{32}{27}

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-1\right), x = 1\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{32}{27}
f=x^2 g=x^3/3 a=plot(f,(x,-5,5)) a.ymin(-5) a.ymax(5) b=plot(g,(x,-5,5)) b.ymin(-5) b.ymax(5) show(a+b) 
       
f=-2*x-8 g=-2*x^2-8*x a=plot(f,(x,-5,5),color='red') b=plot(g,(x,-5,5)) c=solve(f==g,x) show(a+b) show(c) 
       

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = 1, x = \left(-4\right)\right]

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = 1, x = \left(-4\right)\right]