Discuss the continuity of the function on the closed interval. Function Interval 1- x, f(x) = { 1 1 +-X, x > 0 [-2, 4] The function is discontinuous because f(-2) f(4). The function is continuous because lim f(x) and lim f(x) both exist. x--2 X→4¬ The function is continuous because lim f(x) = lim f(x) = f(0) = 1. x-0 オ→o+ The function is continuous because the domain boundary is not inside the interval [-2, 4]. The function is discontinuous because all piecewise functions are discontinuous at their domain boundaries.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.