[3] For the given function, f (x) = ix if x * 0 Oif x =0 evaluate the following: [3.1] lim f (x) x-0 [3.2] lim f(x) x-0+ [3.3] lim f (x) X-0 [3.4] f (0) [3.5] Plot the graph of the function. [3.6] Are there discontinuities in the graph? If there is, at what values of x is the function discontinuous? Show analytical proof for your answer. [4] Prove that each function is discontinuous at the number a. Then determine if the discontinuity is removable or essential (i.e. not removable). [4.1] f (x) = 9x2-4 3x-2 1 0 = = [4.2] f (y) = Vy+5-v5 -;a = 0 [4.3] f (s) = 15+5 1/ S#-5) ;a =-5 0 ifs =-5) [4.4] f (t) = {t" - 4 ifts 2) if t > 2) ; a =2 [5] Illustrated is a function, f(x): f(x) 4 [5.1] Write a piece-wise defined function that will model the illustration. [5.2] At what points is the function discontinuous? Show proof of your answer(s). [5.3] If there are points of discontinuity, which one is an essential discontinuity? Why? [5.4] Which one is a removable discontinuity? Why? [5.5] For your answer in [5.4], what value of f(x) will make it continuous