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Just looking for a yes/no. I worked out the following question:

(A) [tex]e^2[/tex]

(B) [tex]\pi[/tex]

(C) [tex]-(1+3\pi/2, 1+3\pi/2, 0)[/tex]

Did I hit the mark?

I got,(A) Calculate the arc length of the curve [tex]r(t) = (\log t, 2t, t^2)[/tex] where [tex]1 \leq t \leq e[/tex]

(B) Let C be the ellipsed form by intersecting the cylinder [tex]x^2 + y^2 = 1[/tex] and the plane [tex]z = 2y + 1[/tex] and let [tex]\textbf{f}(x,y,z) = (y,z,x)[/tex]. What is [tex]\int_C \textbf{f} d\textbf{r}[/tex].

(C) Let C be the hyperbola formed by intersecting the cone [tex]x^2 + y^2 = z^2[/tex] and the plane [tex]x+y+z=1[/tex] and let [tex]\textbf{f}(x,y,z) = \textbf{k}/z^2[/tex]. What is [tex]\int_C \textbf{f} \times d\textbf{r}[/tex]

(A) [tex]e^2[/tex]

(B) [tex]\pi[/tex]

(C) [tex]-(1+3\pi/2, 1+3\pi/2, 0)[/tex]

Did I hit the mark?

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