Let $Cbe$ the curve defined $by$

$\underset{t{0}^{+}}{lim}r(t)CxyCCr(t)=(tcos(\frac{1}{t}),tsin(\frac{1}{t}),t),0$

$(a)$ Find $\underset{t{0}^{+}}{lim}r(t).$

$(b)$ Draw the projection $ofC$ onto the $xy-$plane. Use $an$ arrow $to$ show

its direction. Then draw $Cin$ space and show its direction $byan$

arrow.

$(c)$ Show that the curve $C$ sits $on$ the surface $of$ a quadratic cone and

find the equation $of$ that cone. Draw the cone and the curve together

$in$ one graph.