1. (5 points) Find an equation of the plane tangent to the sphere $(x+5)^2 + (y+3)^2 + (z+2)^2 = 289$ at the point $(4, 5, 10)$.
2. Let $r(t) = <2 + t^2 \tan t, t + e^{\cos t}, 4 + 7t^6 >$.
(a) (3 points) Is $r(t)$ continuous at $t = 0$? Why or Why not?
(b) (5 points) Find $r'(t)$.
(c) (6 points) Find the angle between $r(t)$ and $r'(t)$ at $t = 0$.
3. Let $p(t) = <2t - \sec^2 t, 5 - 4t^3, te^t >$.
(a) (1 point) What is domain of $p(t)$ that includes $t = 0$?
(b) (5 points) Determine the vector function $\int_0^{\pi/4} p(t) dt$.
