MAT 142 Days 27-28

1270 days ago by kcrisman

Let's see what it looks like to view sequences.  Be sure to use $n$ for your variables for now.

var('n') @interact def _(a=1/n^2,endpoint=20): a(n)=a show(points([[i,a(i)] for i in [1..endpoint]]),figsize=4) 
       

Click to the left again to hide and once more to show the dynamic interactive window

It's possible to see the squeeze theorem, too.

endpoint=10 points([[i,sin(i)/i^2] for i in [1..endpoint]])+plot(1/x^2,(x,1,endpoint),linestyle='--',color='red')+plot(-1/x^2,(x,1,endpoint),linestyle='--',color='red') 
       

We can see the idea of $\epsilon-N$ proofs here.  Plug in your desired values for $eps=\epsilon$, going from $N$ to however far you want to go.  Click "Update" twice to see the new one.

var('n') @interact def _(a=1/n^2,L=0,eps=.1,N=10,endpoint=20,auto_update=False): a(n)=a show(points([[i,a(i)] for i in [N..endpoint]])+plot([L+eps,L-eps],(N,endpoint),color='red',linestyle='--'),figsize=4) 
       
eps 
endpoint 

Click to the left again to hide and once more to show the dynamic interactive window