Exercise (a) Approximate f by a Taylor polynomial with degree n at the number a. Step 1 The Taylor polynomial with degree n = 3 is T3(x) = (a) + f'(a)(x – a) + "(a)(x - a)² + "(a) (x – a)3. 2! 3! The function f(x) = e2x² has derivatives f"(x) = (4x 4r f"(x) = ( 16x² + 4 16. +4 and f"(x) = ( 64x³ + 48x 64 + 48r Jozn? Step 2 With a = 0, f(0) = 1 1,f'(0) = 0 0,r"(0) = and f"(0) = 0. Step 3 Therefore, T3(x) =| 4 Submit Skip (you cannot come back)

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Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.