Demarcus Avery Brewer MAT 265 ONLINE B Fall 2021 Assignment Section_1.5 due 10/24/2021 at 11:59pm MST Problem 1. (1 point) Problem 2. (1 point) Let Le f (x) = x2 + 16 f (x ) = - 4 16-x2 *+8 Find the points of discontinuity of f. For each of them give the Find each point of discontinuity of f, and for each give the value number C at which the discontinuity occurs and the values of both of the point of discontinuity and evaluate the indicated one-sided one-sided limits. Enter INF for co, -INF for -co, DNE for does limits. not exist, CND for cannot determine. If you find more than one point of discontinuity, enter them in order from smallest to largest. NOTE: Use 'INF' for co and '-INF' for -co. If there are answer boxes left unfilled, fill each of them with an 'x'. If you have more than one point, give them in numerical order, from smallest to largest. Point 1: C = If you have extra boxes, fill each in with an 'x'. lim f(x) = -C- lim f(x) = Point 1: C = lim f(x) = Point 2: C = lim f(x) = lim f(x) = X - C+ lim f(x) = Point 2: C = lim f(x) = *- C- Point 3: C = lim f(x) = * - C+ lim f(x) = x -C- lim f(x) = *- C+ Point 3: C = lim f(x) = C- lim f(x) = * - C+ Problem 3. (1 point) A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or not continuous at x = a. 2. f(a) could either be defined or redefined so that the new func- tion IS continuous at x = a. Let f (x ) =2 + -8x + 45 x (x - 5) ' if x # 0,5 if x = 0 Show that f(x) has a removable discontinuity at x = 0 and deter- mine what value for f(0) would make f (x) continuous at x = 0. Must redefine f (0) =_ Hint: Try combining the fractions and simplifying. The discontinuity at x = 5 is actually NOT a removable disconti- nuity, just in case you were wondering