detailed handwritten solution. do not copy from other sites

Let Fa) =

Let F(t) Find F '(t) Let F(t) t2 1, 2e2t, sin(t) > _ t2 + 2, 3et, sin(4t) > Find F(t)dt (don't include the C) Let F(t) = < 2t4 + 3, t5 + 2t4, In(5t) > Find a parametric equation of the line tangent to F(t) at the point (165, 405, 2.708) 165 + 216t z(t) 2e at, sin(t)) Let F(t) Find the unit tangent vector T (t) at the point t o ri(o) = < Find the positive value for which the vector r(t) is perpendicular to r '(t). (4t, 7t2, 9t2 5)