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How to show function is converging towards a point or not.
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Say F is function of n and x. Say F=(n*x)/1+(n*x)^2 Is given function then for x[0,k] where k belongs to (0,1). Show that when n tends to infinity will give converging function. Using graphs. Basically just take limit as n tends to infinity where x belongs accordingly. Please I need code as I am getting few error.
7 Comments
madhan ravi
on 20 Oct 2018
Edited: madhan ravi
on 20 Oct 2018
Upload your code ,x[0,k] what does this mean? Is it a function?
T
on 20 Oct 2018
Edited: T
on 20 Oct 2018
No generally when you find limit on variable x say we find for all values for x but here x belongs to 0<=x<=k.( closed interval [0,k] Where k belong to open interval 0<k<1. Please help me out as I am getting error like how we will define x and k together. Then find limit for n tends to infinity with conditions on x . Using graph we need to observe.
Walter Roberson
on 20 Oct 2018
I suspect that you are missing () in F. No one bothers to write a division by 1,but people do accidentally omit ( for division by (1+something)
T
on 20 Oct 2018
Now find limit when n tends to infinity where x has condition that it will take value between closed interval [k,1] and where k belongs to open interval (0,1) That all I need graph for that particular limit to have clear picture. Please help me with code as I am getting few error.
T
on 20 Oct 2018
Edited: Walter Roberson
on 20 Oct 2018
sysm n,x
X=0:k;
K=(0:1);
y = fun of n and x.
Limit((y),n,inf)
Plot(x,n,y)
Something like this
Accepted Answer
madhan ravi
on 20 Oct 2018
Edited: madhan ravi
on 20 Oct 2018
syms n x k assume(0<k<1) %openinterval assumeAlso(0<=x<=k) %closedinterval F= (n.*x)./(1+(n.*x).^2) limit(F,n,inf) F=@(x,n) (n.*x)./(1+(n.*x).^2) x=linspace(0,1,1000); n=1:1000; plot(F(x,n))
20 Comments
madhan ravi
on 20 Oct 2018
Edited: madhan ravi
on 20 Oct 2018
Yea the difficult part is the graph now , I am figuring it out
T
on 20 Oct 2018
Yes please that will be great bcs once we will have graphs then everything will be clear through graph whether it is converging or not
madhan ravi
on 20 Oct 2018
Edited: madhan ravi
on 20 Oct 2018
syms n x k
assume(0<k<1) %openinterval
assumeAlso(0<=x<=k) %closedinterval
F= (n.*x)./(1+(n.*x).^2)
limit(F,n,inf)
F=@(x,n) (n.*x)./(1+(n.*x).^2)
x=linspace(0,1,1000);
n=1:1000;
F= (n.*x)./(1+(n.*x).^2)
plot3(x,n,F)
xlabel('x')
ylabel('n')
zlabel('F')
grid on
The above will display it in 3d , see attached screenshot
T
on 20 Oct 2018
If you don't mind can you please tell me how to have proper command on Matlab.BCS it is very useful to have proper understanding.
madhan ravi
on 20 Oct 2018
see lots of videos and there is suggested books in mathwork website https://in.mathworks.com/academia/books/mastering-matlab-hanselman.html
T
on 20 Oct 2018
also, we used . while writing function BCS it is a way to express when we do multiplication
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