Does the following function have a limit at a=0? If so, what is it? The limit is 1.
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Does the following function have a limit at a=0? If so, what is it? The function does not exist.
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The next function has a constant k in it that you can change with the slider. Find a value for k so that the limit of the function exists at every point. Answer: k=2, the limit of the function should exist at every point.
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negative 10
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Why does this value for k work? Explain what you see geometrically, and if possible explain algebraically. Answer: This value for k works, as when k=2, the graph becomes a straight line, and so the limit of the function should exist at every point. Algebraically, k=2 would work because when the numerator is factorized, it would equal to (x-2)(x+1), and so the (x-2) would cancel out, leaving the function for a straight line, where a limit would exist for all functions.
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When you are done, save this graph and share it with me (jbowman@smith.edu).
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