Question: a. Derive the linear approximation e x 1 + x at x = 0. b. Estimate to five decimal places the magnitude of the

a. Derive the linear approximation e^x ≈ 1 + x at x = 0.

b. Estimate to five decimal places the magnitude of the error involved in replacing ex by 1 + x on the interval [0, 0.2].

c. Graph e^x and 1 + x together for -2 ≤ x ≤ 2. Use different colors, if available. On what intervals does the approximation appear to overestimate ex? Underestimate e^x?

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