I would like some assistance with the following limits of discontinuity question

b. Determine the discontinuities of the following functions and state why the function fails to be continuous at those points. Check your answers by using a graphing calculator ( such as Desmos) IF(x) = x"-10x+2 ( 4 marks] x-2 ii.F(x) =x3- x? +3 [4 marks] 3. (a) Why is L'Hospital's rule useful for finding the limits? Can it be used in every situation? Please justify your answer? [ 4 marks] (b) Evaluate each limit. Use L'Hospital's Rule where appropriate. i. lim x-256 X+4 X-4 ii. lim *-3x 243 X-9 [3 marks each] (c )Finding an interest rate: Suppose you invest J$ 150,000 in a special 5 year savings account with a fixed annual rate r, with monthly compounding. The amount of money A in the account after Syears (60 months) is: A(r ) = 150,000( 1 + r*=).. Your goal is to have $200,000 in the account after 5 years. i. Use the Intermediate value theorem to show there is a value of r in ( 0,0.07) that is an interest rate between 0%% and 7% for which A(r ) = 200,000. THE UNIVERSITY OF THE WEST INDIES OPEN CAMPUS Page 24 of 40 Econ 1604 Mathematics for Social Sciences II- Course Information. Academic Year 2021/2022. Secrester ? ii. Use a graphing utility to illustrate your explanation in part (i) and then estimate the interest rate required to reach your goal. [5 marks each]