Question: Consider the curve described by the vector function r(t) = (50e -t cos t)i + (50e -t sin t)j + (5 - 5e -t )k,

Consider the curve described by the vector function 

r(t) = (50e-t cos t)i + (50e-t sin t)j + (5 - 5e-t)k, for t ≥ 0.

a. What is the initial point of the path corresponding to r(0)?

b. What is lim r(t)?

c. Sketch the curve.

d. Eliminate the parameter t to show that the surface on which the curve r(t) lies is z = 5 - r/10, where r2 = x2 + y2.

lim r(t)?

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