Number 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 0.85
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Number 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.)
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- Number 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.) e-0.5Number 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.) cos (-0.25)Fast pls solve this question correctly in 5 min pls I will give u like for sure Shub a)Use a Taylor polynomial to approximate 1/√e within an error of magnitude no greater than 0.001 b) Use a Taylor polynomial to approximate ln(1.1) within an error of magnitude no greater than 0.0001
- Dynamic 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 answersTwo 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)Very urgent Numerical method Find the 2nd and 3rd order Taylor polynomials of the function f (x) = cosx around x0 = 0. Calculate the approximate value of cos (0.01). Determine an upper bound for the error in this approximation.
- Approximating sin x Let ƒ(x) = sin x, and let pn and qn be nth-order Taylor polynomials for ƒ centered at 0 and p, respectively.a. Find p5 and q5.b. Graph ƒ, p5, and q5 on the interval [-π, 2π]. On what interval is p5 a better approximation to ƒ than q5? On what interval is q5 a better approximation to ƒ than p5?c. Complete the following table showing the errors in the approximations given by p5 and q5 at selected points.d. At which points in the table is p5 a better approximation to ƒ than q5? At which points do p5 and q5 give equal approximations to ƒ? Explain your observations.NUMERICAL ANALYSIS Use the Taylors method with step size of 0.15 to approximate the solution of ty'-2y-t3et, 1≤t≤2, y(1)=0. Compare the result with actual value y(t)=t2(et-e) . Use the answers generated in Euler’s method and linear interpolation to approximate the following values of y, and compare them to the actual values.1. y(0.75), 2. y(1.2),Using formula attached, approximate ? by a Taylor polynomial with degree ? = 2 centered at 0 and then approximate √4.1 (Round the answer to six decimal places.)
- Find the first several Taylor polynomial approximations of the solution of the differential equation below with initial conditions. Graph the approximations all on one graph, starting with degree 1. y'' +2xy'+y=0 y(0)=2 y'(0)=-2 part B: Find and graph enough Taylor polynomial approximations until two consecutive approximations differ by less than 0.1 for all ? between −0.75 and .75Consider the function f(x) = 3√x. (a.) Approximate f(x) with T2(x), the second degree Taylor polynomial, centered ata= 1. You do not need to expand/simplify the polynomial. b.) Use Taylor’s Inequality, to estimate the accuracy of your approximationwhenxis within the interval 0.5≤ x≤ 1.5. Round the maximum error|Rn(x)|to 3 decimal places.Assume that g(x)= 1/x, 0.4≤x≤1.6. Assume that you approximate g(x) by the 2nd degree Taylor polynomial T2(x) which is centred at a=1. Taylor's inequality gives us an estimate for the error that is involved with this approximation. Now, find the smallest possible value for the constant M that is referred to in Taylor's inequality. The answer is no -6.