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2. Consider the function f(x) = e^(2(xâ1)) near x = 1.
(a) Find the local linearization of f(x) near x = 1.
(b) Use the local linearization to estimate e. (Hint: f(3/2) = e^(2(1/2)) = e^1 = e.)
(c) Find the Taylor polynomial of degree 2 approximating f(x) near x = 1.
(d) Use the Taylor polynomial of degree 2 to estimate e.
(e) Find the Taylor polynomial of degree 3 approximating f(x) near x = 1.
(f) What is the Taylor series for f(x) near x = 1? (Your answer should include the first four nonzero terms, but you do not need to find a formula for the general term or use sigma notation.)
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