Please write the detail steps of question3. Thank you so much.

1. 

thmetic in part (b). Don't expand the powers (x - (b) Use the approximation f(x) ~ To(x) to estimate v2. Express your estimate as a ratio of integers in lowest terms (i.e. a reduced fraction). 2. (a) Find the degree 6 Taylor polynomial, To(x), of the function f(x) = Vx, centered at the point a = 4. (b) Use the approximation f(x) ~ To(x) to estimate v2. Express your estimate as a ratio of integers in lowest terms. 3. (See Example 11, pp. 808-809) Let f ( z) = 1 0 sin (z2) pme- know x = 0 exp (a) Why is f continuous at x = 0? (b) Use the Maclaurin series for sin x to find the Maclaurin series for f (x). (c) Evaluate the indefinite integral f f(x) da as an infinite series. (d) Use part (c) to express the definite integral fo f(x) dx as an infinite series. (e) Estimate the sum of the series in part (d) by the fifth partial sum, and express your estimate as a decimal number. Use the Alternating Series Estimation Theorem (p. 775) to find a bound on the error