For the function f bellow evaluate lim f(x), lim f(x), lim f(x), and x→2- x→2+ x→0- lim f(x). Find all points where f is not x→0+ continuous. At which of these values is f continuous from the right, from the left or neither? Explain using the definition of continuity. Show your work. ( 2x + 5, if x < 0 x² – 1, if 0 < x < 2 f(x) = { x + 1, if x > 2

Q: 3 Use the Squeeze Theorem to evaluate lim f(x), where f(x)=x²cos (-). x A B C D - 0 0 1 8 -0-x

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A: Suppose that f is a function such that, limx→∞fx-2x2=π.  To determine, limx→∞ fxx2+1, if possible.

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A: For a function to be continuous at a given point,it should be defined at that point and its limit…

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A: The solution of above question is written below.

Q: Determine which one of the following rules for continuity is first violated at a = – 1. | O f(a) is…

A: From the graph we see that f(-1)=-2So, f(-1) is defined and "f(a) is defined" is not violated.