(4) All of the statements below are false. Produce a counterexample for each to show that the statement is false. You can simply draw a picture to illustrate the counterexample. (Reminder: a counter example is an example where the statement's conclusion does not hold.) (a) If f(3) = 7, then lim f (x) = 7. (b) If f(2) is undefined, then lim f (x) is undefined. (c) If lim f(x) and lim f(x) both exist, then limx-to f (x) exists. x -+ 0+ x-+0- (d) If lim f(x) = 2 then f (5) = 2. x-+5(c) Fill in the blank. Enter \"DNE\" if the requested limit does not exist. gym = $35)" (3 + m2) = 335 M) = y = r) a: 4321 12345678 (1) For each part, write an equation that the point (3:, y) must satisfy. (a) The distance from (2, 1) to (m, y) is equal to the distance between the points (1, 5) and (4, 1). (b) The line containing (any) and (3, 2) is perpendicular to the line given by y = 5:6 1. (2) Find the point(s) of intersection of the line through the points (5, 1) and (1, 5) and the circle given by m2+y22m6y+2=0