I seem to be having some trouble with the Sinc[x] function, and I think it's due to rounding, but I'm not sure.

The code is below, with relevant constants:

b = 0.1; a = 8.7106181548*^-18; alpha$of$r[r_] := alpha /. FindRoot[alpha - b * alpha + (b/a) * Sin[a * alpha] == r (1 - 2 * b), {alpha, r (1 - 2 *b)}]; u[r_] := b * Sinc[a * alpha$of$r[r]]; Plot[b - u[r], {r, 10^9, 10^10}] 

When we plot the function u[r] in the range specified, it does not seem to return a continuous curve as expected. The picture of the plot is shown here: http://i.imgur.com/6R2VsYz.png.

Could anyone offer insight as to why this happens and how I could fix it? I apologize in advance if I'm missing any information, as I'm new here. Thanks!

I seem to be having some trouble with the Sinc[x] function, and I think it's due to rounding, but I'm not sure.

The code is below, with relevant constants:

b = 0.1; a = 8.7106181548*^-18; alpha$of$r[r_] := alpha /. FindRoot[alpha - b * alpha + (b/a) * Sin[a * alpha] ==  r (1 - 2 * b), {alpha, r (1 - 2 *b)}]; u[r_] := b * Sinc[a * alpha$of$r[r]]; Plot[b - u[r], {r, 10^9, 10^10}] 

When we plot the function u[r] in the range specified, it does not seem to return a continuous curve as expected. Here's a picture of the plot:

Could anyone offer insight as to why this happens and how I could fix it? I apologize in advance if I'm missing any information, as I'm new here. Thanks!