2_ Q8. Given 3: = u 1 and u = Exfxg + 2, nd :3. u2+1 Q9. Find all derivatives yin) of the function y = rm3 7x. Q10. (Parametric Equations) Consider the folium of Descartes described by the equation x3 + 2.0 L5 1.0 Figure I 3:3 3x3; : 0 as shown in (i) Assuming x :> 0, y :> 0, nd the point P(xo, yo) where the tangent to the curve at that point is horizontal. (ii) What are the parametric equations for the folium, x = t), 3: = g(t)? (iii) By using the parametric equations in (ii), what is the corresponding value for the parameter t = to for the point P050, yo) in (i)? Check that the value of to obtained is consistent with the results in (i) and (ii), i.e., x0 = f(tn),y0 = 9(t0). (v) Write a Mathematica code to generate the folium of Descartes in Fig. 1. Q11 (Related rates) (a) If an object is moving on the curve y : x3, at what point(s) is the y-coordinate of the object changing three times more rapidly than the sic-coordinate? (b) If the diagonal of a cube is increasing at a rate of 3 cubic inches per minute, how fast is the side of the cube increasing? Q12. (Differential) It is desired to give a spherical tank of diameter 20 feet (240 inches) a coat of 0.1 inch thick. Estimate how many gallons of paint will be required, if 1 gallon is about 231 cubic inches. Note: You are supposed to use approximation hV x (W instead of doing an exact calculation