Consider the curve described by the following vector function r(t)= (50 e⁻ᵗ cos t)i + (50 e⁻ᵗ sint)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)? t-[infinity] r where 2x²+y²?
c. Eliminate the parameter t to show that the curve r(t) lies on the surface z= 5-r/10, where r²= x²+y².