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Matching In Exercises 19-22, match the Taylor polynomial approximation of the function
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Calculus: An Applied Approach (MindTap Course List)
- 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_forwardTaylor polynomials Find the nth-order Taylor polynomial for the following functions centered at the given point a. ƒ(x) = e1/x- 1, n = 2, a = 1arrow_forwardDynamic profit function is P(t)= 2 - (t - 5) x ln (t + 1), here t is measured in years, and P is measured in hundreds of euros. a) use marginal analysis to estimate how fast company's profit was growing initially b) use Taylor formula to write down square approximation of the given profit function around t=2. Round coefficient of the Taylor polynomial to 3 decimals c) use results from step b) to estimate total company's profits between first and fourth years of operation d) estimate average company's profit between first and fourth years of operation e) use initial function to estimate total company's profits between first and fourth years of operation. Compare results with step c) the question is not graded, as the exam was yesterday, I want to check my answersarrow_forward
- numerical solution B. Find the interpolating polynomial of the following point and function using Lagrange interpolation process.1. (-3,0), (-1,2), (0,-2), (1,3) and (3,-1). 2. y = cos ( 2x ) at x = [0,π] with four equally spaced points.arrow_forwardNUMERICAL ANALYSIS A car traveling along a straight road is clocked at a number of points. The data from the observations are given in the following table, where the time is in seconds, the distance is in feet, and the speed is in feet per second. Time 0 3 5 8 13 Distance 0 225 383 623 993 Speed 75 77 80 74 72 Use a Divided difference scheme to predict the position of the car and its speed when t = 10s. Use the derivative of the polynomial to determine whether the car ever exceeds a 55 mi/h speed limit on the road. If so, what is the first time the car exceeds this speed? What is the predicted maximum speed for the car using appropriate coding scheme?arrow_forward
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