Give algebraic formulas for functions that satisfy each set of conditions below. (One function per part; each part is independent from the other parts.) Make sure you explain why each of your examples satisfies all conditions, by showing the appropriate limit calculations. You are allowed to use piecewise definitions, but try to keep your examples as simple as you can. (a) A function f(x) with exactly one horizontal asymptote and is continuous everywhere. (b) A function f (x) that has exactly one infinite discontinuity and exactly one removable discontinuity. (Note: infinite discontinuities are also known as essential discontinuities.) (c) A function f(x) that has exactly one jump discontinuity and satisfies

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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.