(a) Graph both e and its linear approximation on the same plot, displaying a values in the interval [0, 2]. What is the exact value of e0.1 and its approximate value from your linear approximation? Compute the relative error. (b) Find a quadratic approximation to f(x) = e near x = 0. Graph both e and its quadratic approximation on the same plot (using the same scale as be- fore). What is the approximate value of e0.1 from your quadratic approximation? Compute the relative error. (c) We can continue to add terms to our approximation. Find a formula for the "cubic approximation" C(x) of a function g(x) around x = c. You should leave your answer in terms of g and its derivatives. (d) Repeat the previous two steps but for a cubic approximation using the formula you found in the previous step. What is the approximate value of e0.1 using your cubic approximation?

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