consider the function g(x) =   2 − πx         if x ≤ a               x^4              if x > a  Show that there exists a value of a which makes g(x) continuous everywhere. (Hint: Draw the graphs of y = 2 − πx and y = x 4 on the same axes. For a particular value of a, the graph of g(x) looks like y = 2 − πx for x ≤ a and y = x 4 for x > a. Based on the graphs, how should you choose a so that g(x) is continuous? Use the IVT to justify that there is such a number a.)

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Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

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