Upgrade to access all content for this subject

On what set is the curve defined by:

$${\bf f}(t)=e^t \sin^4 t {\bf i} + t^2 e^{ \cos ^4 t} {\bf j} + e^{t} {\bf k}$$

...smooth?

$(0, \infty)$

$(-\infty, 0)$

$(-\infty, 0)$ and $(0, \infty)$

$(-\infty, \infty)$

$(0,1)$