7. Given x = 5cost and y = 4sint, find in terms of t a) dy dx [4] b) d2 y dx2 [5] 8. A curve is defined by parametric equations x = t2 + t - 1 and y = 2t2 - t + 2 for all t i. Show that A(-1,5) lies on the curve [4] ii. Find dy [4] dx iii. Find the equation of the tangent to the curve at the point A [5] 9. Find the constant m ify = emx satisfies day dx2 - 52 dy + 6y = 0 [8] 10. Using the Substitution u = 2x - 1, prove that J X (2x-1)3 dx = 25 [1 11. Find S2 ex sin x dx