Does 1/(e^x^2) converge?

Does 1/(e^x^2) converge?

The notation is ambiguous, so we consider both interpretations:

(a) `1/e^(x^2) ` converges. The terms as x increases without bound go to zero. The denominator increases without bound as x increases without bound and the numerator is constant.

The graph:

(b) If what was meant was `1/(e^x)^2=1/e^(2x) ` this also converges for the same reason. The graph:

Note that this function converges as x increases without bound -- as x decreases without bound the function diverges.