Matching In Exercises 5-8, match the Taylor polynomial approximation of the function
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- Think About It Sketch the graph of a fifth-degree polynomial function whose leading coefficient is positive and that has a zero at x=3of multiplicity 2.arrow_forwardTwo parts to this question. Find the second-degree Taylor polynomial for f(x)=√x f(x)=x centered at x=4 p2(x)= Use p2(x) to approximate squareroot(4.1)arrow_forwardNumber of terms What is the minimum order of the Taylor polynomial required to approximate the following quantities with an absolute error no greater than 10-3? (The answer depends on your choice of a center.) ln 0.85arrow_forward
- Using Newton’s Method In Exercises 123–128, useNewton’s Method to approximate the zero(s) of the function.Continue the iterations until two successive approximationsdiffer by less than 0.001. Then find the zero(s) using a graphingutility and compare the results.123. f (x) = x3 − 3x − 1arrow_forwardSurface Area The roof over the stage of an open air theater at a theme park is modeled by f(x, y) = 25[1 + e−(x2+y2)1000 cos2(x2 + y2/ 1000 )] where the stage is a semicircle bounded by the graphs of y = √502 − x2 and y = 0. Use a computer algebra system to approximate the number of square feet of roofing required to cover the surface.arrow_forwardFill in the blanks. a. In the polynomial regression equation y = 5 + 3x− 2x2 + 7x3 + 9x4, the cubic effect coefficient is ________. b. In polynomial regression, we usually ________.a predictor variable to reduce the correlations between its powers. c. In the forward selection method of polynomial regression, we add increasing powers of the predictor variable until the t-test for the utility of the highest-degree term is ________. d. The second-order polynomial regression equation relating a response variable y to two predictor variables x1 and x2 is given by _______.arrow_forward
- f is a polynomial function of degree 3 whose coefficients arereal numbers; its zeros are 2, i, and 3 + i.arrow_forwardTrue or False In Exercises 81 and 82, decide whetherthe statement is true or false. Justify your answer.81. It is possible for a third-degree polynomial functionwith integer coefficients to have no real zeros.82. If x = −i is a zero of the functionf(x) = x3 + ix2 + ix − 1then x = i must also be a zero of f.arrow_forwardFill in the blanks.a. In the method for polynomial regression, increasing powers of the predictor variable are added until the t-test for the utility of the highest-degree term is not signicant.b. In the method of polynomial regression, if the t-test for the utility of the highest-degree term is not signicant, then that term is removed from the regression equation.c. In the second-order polynomial regression equation involving predictor variables x1 and x2, the cross-product term is given by .d. In a term involving a product of powers of predictor variables, the sum of the powers is called the of the termarrow_forward
- Taylor polynomials Find the nth-order Taylor polynomial for the following functions centered at the given point a. ƒ(x) = cos3 x, n = 2, a = 0arrow_forwardf is a polynomial function of degree 3 whose coefficients are real numbers; its zeros are 4 + i, 4 - i, and 2 + i.arrow_forwardFill in the blanks. a. In the method for polynomial regression, increasing powers of the predictor variable are added until the t-test for the utility of the highest-degree term is not significant. b. In the method of polynomial regression, if the t-test for the utility of the highest-degree term is not significant, then that term is removed from the regression equation. c. In the second-order polynomial regression equation involving predictor variables x1 and x2, the cross-product term is given by . d. In a term involving a product of powers of predictor variables, the sum of the powers is called the of the term.arrow_forward
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