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Category > Math Posted 19 Apr 2017 My Price 8.00

MATH 3B3 (Fall 2016)

Please help me out to figure out the solution... in details.

I was sick last two weeks that i didnt attend school, so i dont know how to do the problems. 

 

 

MATH 3B3 (Fall 2016)
Assignment 1
Due Date: Before 12:30 pm, September 23, 2016
1. Let γ(t) : [a, b] −→ R3 be a C 1 curve. Show that its arclength is independent of reparametrization. [Hint: Use the fact explained in class that a
reparametrization is either monotonically increasing or decreasing. In each
case use the formula for integration by substitution.]
2. For the curve c(t) = (et cos t, et sin t, et ) with t > 0, find its reparametrization by arclength.
√
√
3. Verify that the curve c(s) = √15 ( 1 + s2 , 2s, log(s + 1 + s2 )) has a unit
speed parametrization. Then compute its curvature and torsion. In this
course, log always refers to the logarithm base e.
4. A regular curve c(t) has the property that there is a vector a ∈ R3 such
that c(t) − a is always perpendicular to its tangent vector c′ (t). Prove that
c(t) must lie on a sphere.
5. Show that the formula
Ï•(u, v) = (u cos v, u sin v, u + v)
for u, v ∈ R gives a parametrization of a regular smooth surface. Find the
equation of the tangent plane and the unit normal vector to the surface at
the point (u, v) = (a, b). 1

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ComputerScienceExpert
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Status NEW Posted 19 Apr 2017 02:04 AM My Price 8.00

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