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Let f(x, y) = x2 + y and let c→(t) = (et, e-t).
a. Compute (d/dt) f(c→(t)) using the Chain Rule.
b. Compute (d/dt) f(c→(t)) without using the Chain Rule, but instead first writing the composition f(c→(t)) as a function of t, then differentiating with respect to t in the usual Calc I way.
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For the region bounded by y =2x2, y = 8, 0 ≤ x ≤ 2, please Sketch the region. Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region about the y-axis.
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