1.) Given: r(t)=tcos(t)i+e(t^2)j+ln(t)k,
what is r'(t)?
2.) Suppose r(t) is a vector-valued func.,
What geometric/graphical info does r'(a) tell us?
3.) Let r(t)=cos(t)i+sin(t)j and s(t)=sin(5t)i+cos(5t)j.
(a) What does the graphs of r(t) and s(t) look like?
(b) Suppose the graphs of two vector-valued func. r(t) and s(t) are the same, then must r'(0)=s'(0)? (Explain whether this is a new result, or was it also true for functions f(x) and g(x)?)