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Problem Set 7: Mathematics Solutions, Assignments of Analytical Geometry and Calculus

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.

Typology: Assignments

2009/2010

Uploaded on 02/24/2010

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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) =<Zu
0p1t2dt, u2
2,0>
Find the domain of Rand show that kR0(u)k= 1 for any uin the domain
of R.
(3) Suppose that R00(u) =<0,0,9.8>,R(0) =<0,0,0>and
R0(0) =<1,0,2>. Find R(u). Find u > 0 so that R(u) =< a, b, 0>. For
this value of u, what are aand b? How can this differential equation be
interpreted?
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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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