1. Consider the differential equation ydxdy=(x+3)(y2+3). Solve this differential equation and find the equation of the curve that passes through point (-6,-2).

2. Consider a function f defined by f(x)=1+4x on [3,5]. By subdividing the given interval into 4 sub-intervals of equal width and considering the midpoint of each of the sub-intervals, calculate the Riemann sumSR4=i=14f(ci)xi

3. Neglecting air resistance, the acceleration of a falling object is g = 9.81m/s2. An object is thrown upwards with an initial speed of 10m/s from the top of a 400m cliff.

a) Determine the function giving the speed of the object.

b) Determine the function giving the position of the object relative to the ground.

c) How long did it take for the object to reach its maximum height?

d) What was the speed of the object when it hit the ground?