Suppose that f(x) is a continuous function with f( – 5) = - 3 and f( – 1) = 3. Determine which choice best describes the following statement. "For some y in the interval [-3,3], f(x) = y for all x in the interval [-5, -1]" || Sometimes true and sometimes false Always false Always true

Q: 3. There are two conditions that must be met in order for a function to be continuous, explain those…

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Q: Determine the end (long run) behavior for the function below: f(x) = x - 3x³ + x – 1 Select the…

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Q: Find the values of a and b that make f continuous everywhere. b = f(x): x-2 ax² - 6x + 3 4x -a + b…

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Q: F(x) = x 1 + 3x2 - — 16х — 20 y 100 50 X - 10 -5 -50! (a) From the graph, estimate where f"(x) > 0.…

A: a) f"(x)>0 By looking at the graph we can conclude that it between the point (0 to -5). As the…

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Q: A relation consists of all the points in the x-y plane that are either on the line y=1 or the line…

A: Here, the objective is to determine if equation represent a function.

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Q: t) For each of the following functions, state whether they are one-to-one or not. (You must enter T…

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Q: There are 3 conditions that make a function continuous at a point.  Name the three conditions Give…

A: Definition: A function is said to be continuous at x = a provided all three of the following are…

Q: Suppose that f(x) is a continuous function with f(4) = -8 and f(8) = 8. Determine which choice best…

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Q: Suppose that f(x) is a continuous function with f(1) = - 6 and f(5) = 6. Determine which choice best…

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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.