Does the curve $(t^2, t^5)$ have a tangent at the origin? My question is whether or not the curve $x(t) = t^{2}, \ y(t) = t^{5}$
has a tangent at $(x, y) = (0, 0)$. 
I don't really know what to do if both $dy = dx = 0$, so I tried to take the limit $\lim_{t \to 0} \frac{dy}{dx} = \lim_{t \to 0}\frac{5t^{4}}{2t}$ which is zero. But does this mean the curve has a tangent, with slope $0$? My book is very unclear with this situation. Thanks!

Note that since


*

*$x'(0)=y'(0)=0$


we can conclude that the origin is  a possible singular point and that is indeed precisely the case since $\frac {dy}{dx}$ is not defined at the origin.
