Answer the following question.

Integrity Tutorial (5.2) C 1. Given F(t) = 2ti + (t2 + 3)j + (2t2 + 5)k, d2 F find (i) , (ii) a 2, (iii) at and (iv) d2 F at2 when t = 1. 2. If F(t) = thi - tj + (2t + 1)k and G(t) = (2t - 3) i+ j -tk, find (i) at (F . G) and (ii) at ( F X G). 3. Find the velocity, speed and acceleration of the particle r(t) = e-ti + 2 cos 3t j + 2 sin 3tk when t = 0. 4. If F(x, y) = (exy)i+ (x - y)j + (x sin y)k, find (ii) Fxx, Fyy and Fyx- 5. If F(t)=sin ti - cost j + tant k, evaluate J TAF(t) dt. 6. If v'(t)=(2t + 1)i - 3t2j + 8t3k, and v(0)=2i + 5j + k, find v(t)