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

Q: The graph of a function f(x) is given below: +3 There is a removable discontinuity at which of the…

A: Given the graph of the function f(x) . To the point where there is removable discontinuity .

Q: Given the following piecewise function, demonstrate how to determine if f(x) is continuous on the…

A: determine if f(x) is continuous on the interval (-6, 6).

Q: 3. Is the following piecewise function continuous or not continuous? Jxl, if x - 2 a. continuous b.…

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Q: (d) lim f(x X →+00

A:

Q: Consider the function below. Use it to evaluate each of the following expressions. (If an expression…

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Q: Which of the following functions have a graph that does not have a vertical asymptote? Select all…

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Q: Sketch the graph of the following function and find any discontimuities x2-1 f(x) = %3D x-1

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Q: Sketch the graph of the following function and find any discontinuities x2 – 1 f(x) = x - 1

A: fx=x2-1x-1 Since the value of numerator and denominator is zero when x=1, therefore the graph must…

Q: Which of the following functions has all of the following features? One negative x-intercept…

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Q: a) Find the domain of following piecewise function. x+1, if-1 s<4 3x-1, ifx 24 f) = b) Determine…

A: We have f(x)=-x+1,    if -1≤x&lt;43x2-1,    if x≥4 Now as we know Domain of a function is the set of…

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.