If the claims on sin(x)/x are right, then the derivative of any function f(x) at any point x0 is not defined at x0. Then, you are taught that you get the result by using the same limit idea. (f(x)-f(x0))/(x-x0) when x is not x0, because otherwise, you get the same 'not defined' 0/0. I have mine as the third pedal in a short chain. I don't notice any tone suck with mine, and mine is unmodified. Solder your capacitor across those two pads. Would you not be allowed to call the function sin(x) continuous because some may want to define itįor the very important concept of derivative, you first compute the ratio Get a cable, insert it into the socket and buzz between the tip and the solder points on the PCB until you get continuity. They could, but why should they when the definition is simply sin(x)/x for all x and the previously uncertain value at x=0 has been solved long ago by the smart idea of limits? Why? Because some may want to define the function Why is it not defined after people solved what previously 'had no solution?'

IMHO, this simply kills the smartness, applicability, and beauty of Math.

However, for some reason, people still tell you that sin(x)/x is not defined at x=0. You take your hat off fo the genius of Math, to make sure you compute the limit from the left and the limit from the right and find them equal 1 and so, now, you may think that you can plot the continuous function f(x)=sin(x)/x for all values, including x=0. You want to use the function f(x)=sin(x)/x and you find out that you can compute all its values, except for x=0, where you get 0/0, and that people call this 'f(x)=sinx/x is not defined at x=0.'īut then, you also learn that smart Mathematicians have managed to find a solution by introducing the concept of limit: lim(x->0)=1.

Where to get continuity mod