MATH 21A Midterm: MATH 21A Harvard 21a summer 10Practice1
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Name: start by printing your name in the above box, try to answer each question on the same page as the question is asked. If needed, use the back or the next empty page for work: do not detach pages from this exam packet or unstaple the packet, please try to write neatly. Answers which are illegible for the grader can not be given credit: no notes, books, calculators, computers, or other electronic aids are allowed, problems 1-3 do not require any justi cations. For the rest of the problems you have to show your work. Even correct answers without derivation can not be given credit: you have 180 minutes time to complete your work. The line ~r(t) = ht, t, ti is perpendicular to the plane x + y + z = 10. The quadratic surface x2 + y2 + z2 = 1 is a one sheeted hyperboloid.
