Devoir NYA

845 days ago by zigong

f(x)=(6*x^3-12)/(12*x^2-6);f(x) 
        
(6*x^3 - 12)/(12*x^2 - 6)
(6*x^3 - 12)/(12*x^2 - 6)
asymptotesVerticales=solve(12*x^2-6,x);asymptotesVerticales 
        
[x == -1/sqrt(2), x == 1/sqrt(2)]
[x == -1/sqrt(2), x == 1/sqrt(2)]
limit(f(x),x=1/sqrt(2),dir="plus") 
        
-Infinity
-Infinity
limit(f(x),x=1/sqrt(2),dir="minus") 
        
+Infinity
+Infinity
limit(f(x),x=1/sqrt(2)) 
        
und
und
limit(f(x),x=-1/sqrt(2),dir="plus") 
        
+Infinity
+Infinity
limit(f(x),x=-1/sqrt(2),dir="minus") 
        
-Infinity
-Infinity
a1=limit(f(x)/x,x=infinity);a1 
        
1/2
1/2
b1=limit(f(x)-a1*x,x=infinity);b1 
        
0
0
asymptote1(x)=a1*x+b1;asymptote1(x) 
        
x/2
x/2
a2=limit(f(x)/x,x=-infinity);a2 
        
1/2
1/2
b2=limit(f(x)-a1*x,x=-infinity);b2 
        
0
0
asymptote2(x)=a2*x+b2;asymptote2(x) 
        
x/2
x/2
P1=plot(f(x),(x,-4,4)) 
       
P2=plot(asymptote1(x),(x,-4,4),rgbcolor=(1,0,0)) 
       
P3=plot(asymptote2(x),(x,-4,4),rgbcolor=(1,0,0)) 
       
oishow(P1+P2+P3,ymin=-10,ymax=10) 
       
P4=plot(f.diff(x),(x,-4,4),rgbcolor=(1,0,0)) 
       
P5=plot(f.diff(x,2),(x,-4,4),rgbcolor=(0,1,0)) 
       
show(P1+P4+P5,ymin=-10,ymax=10)