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Solutions to problem set 7, which includes calculus problems related to finding equations for tangent lines, analyzing functions and their derivatives, and solving differential equations.
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Problem Set 7, Due Eighth Class Meeting
(1) Find an equation for the line tangent to the helix H(t) =< cos(t), sin(t), t > at the point when t = π/4. (2) Consider the function
R(u) =<
∫ (^) u
0
1 − t^2 dt, u^2 2
Find the domain of R and show that ‖R′(u)‖ = 1 for any u in the domain of R. (3) Suppose that R′′(u) =< 0 , 0 , − 9. 8 >, R(0) =< 0 , 0 , 0 > and R′(0) =< 1 , 0 , 2 >. Find R(u). Find u > 0 so that R(u) =< a, b, 0 >. For this value of u, what are a and b? How can this differential equation be interpreted?
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