A function f(x) is continuous at a point x = a if lim f(x) = x-a...

 

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A function f(x) is continuous at a point x = a if lim f(x) = x-a Consider the function f(x) = = { 8 cos (2) 64|x| x²-8x Is the function continuous at x = 0? We first evaluate the limit of f(x) at x = 0. The right-sided limit is: lim f(x) = x→0+ while the left-sided limit is: lim f(x) = x-0¯ for x ≥ 0, for x < 0. As a result, the limit is (enter DNE if the limit does not exist): lim f(x) = x→0 The value of the function at x = 0 is: f(0) = and thus we conclude that f(x) is at x = 0. lim f(x) = x→0¯ As a result, the limit is (enter DNE if the limit does not exist): lim f(x): x→0 The value of the function at x = 0 is: f(0) = and thus we conclude that f(x) is at x = 0. A function f(x) is continuous at a point x = a if lim f(x) = x-a Consider the function f(x) = = { 8 cos (2) 64|x| x²-8x Is the function continuous at x = 0? We first evaluate the limit of f(x) at x = 0. The right-sided limit is: lim f(x) = x→0+ while the left-sided limit is: lim f(x) = x-0¯ for x ≥ 0, for x < 0. As a result, the limit is (enter DNE if the limit does not exist): lim f(x) = x→0 The value of the function at x = 0 is: f(0) = and thus we conclude that f(x) is at x = 0. lim f(x) = x→0¯ As a result, the limit is (enter DNE if the limit does not exist): lim f(x): x→0 The value of the function at x = 0 is: f(0) = and thus we conclude that f(x) is at x = 0.