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1.   Find the curvature, \(K\), for the curve \({\bf r}(t) = \langle t, t^2, t^3 \rangle\) at \(t = 1\).

a.  \(\frac{1}{2} \)

b.  \(\frac{1}{\sqrt{2}}\)

c.  \(\frac{\sqrt{19}}{7\sqrt{14}}\)

d.  \(\frac{\sqrt{19}}{\sqrt{14}} \)

e.  \(\frac{1}{\sqrt{14}} \)

2.   Find the length of the curve \(C:\vec{r}(t) = \langle \cos t, \sin t, \frac{3}{4}t \rangle \) where \(0 \leq t \leq 4\pi\).

a.  \(\pi\)

b.  \(2\pi\)

c.  \(3\pi\)

d.  \(4\pi\)

e.  \(5\pi\)