FINAL ASSIGNMENT - QUESTION 1 1. (a) Without using a caieulatorr.' determine the following integral: 1 3:" 2:1: 5 L m \"'3- (H'mt: First write the integrand 1(1) as 1222+5 _1+ I117+b 13 + 22 + 5 1:3 + 2: + 5 where a. and b are to be determined.) 1(1) = (h) A steel storage tau]: for propane gas is to be constructed in the shape of a. right circular cylinder with a hemispheze at each end. Suppose the cylinder has length 3? metres and radius r metres. (i) Write down an expression for the volume V of the storage tank (in terms of E and r}. (ii) Write down an expression for the surface area A of the storage tan]: (in terms of f and r}. (iii) Using the result of part [ii], write V as a function of r and A. (That is' elinunste E.) (iv) A client has ordered a tan}; but can only afford a tank with a surface area of A = 10!] Square metres. Given this constraint' write V = V(r]. {v} The client requires the ten]: to have volume V = 40 cubic metres Use Newton's method, with an initial guess of r0 = 4 to nd an approximation [accurate to three decimal places) to value of r which produces a volume of 40 Cubic metres. [Newton's method lim- solv-ing r] = U: \"+1 = '\" ' n.) for {i=04112,_._]