A is what I said was constant,and it is, with respect to the transform of the original rectangle function, others in this thread have quoted x as being constant. This also is valid when speaking of l'hopitals rule in part because the partial derivative of sinc with respect to A was taken.
Also...
It it? I think many other people like me who don't exactly understand how it works would phrase the question in a similar manner, hence the quotes for constant.
Yes that is a good point, i like the analysis. I guess what I would like to know now then, is whether I can indeed use l'hopitals rule in the way I have, using A as the variable in the analysis of the limit(taking derivatives with respect to A), even though sinc was originally a function of x.
I believe you are correct cp255, I am just lacking in formal proof.
cpscdave - x is inversely proportional to A, so the sin function approaches zero, but, the denominator of the sinc function (it is the sinc function not the sin function) approaches zero also...need some sort of formal analysis...
Perhaps I should include that the sinc function is the Fourier transform of the ractangle function of height A and width 1/A, hence why A is 'constant'...but not...in this question.
Homework Statement
Determine limA→∞(sinc(x/2A))
Homework Equations
I would use L'Hôpital's rule, but I'm not sure if it is valid in this case as the function is that of x, not A. I want to know if it's valid to treat x as constant and take derivatives with respect to A and evaluate as...