If u and v are differentiable vector functions, c is a scalar, and f is a real-valued function, write the rules for differentiating the following vector functions. (a) u(t) + v(t) (b) cu(t) (c)f (t) u (t) (d) u(t) . v(t) (e) u(t) x v(t) (f ) u (f (t))

Pls answer no. 6

a. Sketch the graph of r(t) = ti+t2j. Show that r(t) is a smooth vector-valued function but the change of parameter t = 73 produces a vector-valued function that is not smooth, yet has the same graph as r(t). b. Examine how the two vector-valued functions are traced, and see if you can explain what causes the problem.