Find the first four distinct Taylor polynomials about
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Calculus Early Transcendentals, Binder Ready Version
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Precalculus: Mathematics for Calculus - 6th Edition
Precalculus Enhanced with Graphing Utilities (7th Edition)
- Write the polynomial p(x) = x³ – 3x² + x − 9 as a Taylor polynomial centered at 20 = 1.arrow_forwardFind the fourth Maclaurin polynomials for f(x) = ex and g(x) = e2x . Explain how you can use the fourth Maclaurin polynomial for f to find the fourth Maclaurin polynomial for g.arrow_forwarda. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. f(x) = 8x³/2, a = 1; approximate 8(1.73/2) a. p₁(x) = b. p₂(x) = c. Using the linear approximating polynomial to estimate, 8 (1.73/2) is approximately (Simplify your answer.) Using the quadratic approximating polynomial to estimate, 8(1.73/2) is approximately. (Simplify your answer.)arrow_forward
- For the polynomial below, 1 is a zero. h (x) =x' + 3x- 7x + 3 = Xarrow_forwardfind the polynomial of the specified degree that has the given zeros. the coefficient of the leading term is 1. assume a=1 and make sure to expand f(x) all the way no parentheses degree 3; zeros -3, -1, 2 also write the polynomial in expanded formarrow_forwardGiven a function f (x) that passes through the points (1, 2), (2,−1), and (3, 4), use the Lagrange interpolating formula to construct a second-degree polynomial that interpolates f at the given points.arrow_forward
- The Lagrange polynomial passes through three data points (3, 11), (9, 10), (26, 21). Find p2(x) at x = 5. Round-off your answer to 3 decimal places.arrow_forwardIn a hospital, a drug is given to a patient. Let f(t) be the amount of drug (in mg) in the patient's body t minutes after it is administered. The nurses want to predict how the body will absorb the drug (the shape of the graph y = f(t)) to be able to prepare the next course of action. One of them remembers about Taylor polynomials from their Calculus course and explains that they allow to predict the shape of a function by making very accurate measurements of the function at one point. They decide to do this and they find the following details about the patient's absorption of the drug: • f(15) = 140 • f'(15) = -10 • f" (15) = 12 1 000 Use these details to approximate the average amount of drug in the patient's body over the first 2 hours: 120 1 f(e) dt 120 Important: Remember that the measurements were made at t = 15 minutes.arrow_forwardfind the taylor polynomial of the nth degree( n=3) and x=0. then find the error estimate for the remainder. x=3 f(x) = (x+1)1/2arrow_forward
- Find the nth Maclaurin polynomial for the function.arrow_forwardLet s(t) be the distance of a truck to an intersection. At time t = 0, the truck is 60 m from the intersection, travels away from it with a velocity of 24 m/s, and begins to slow down with an acceleration of a = −3 m/s2. Determine the second Maclaurin polynomial of s, and use it to estimate the truck’s distance from the intersection after 4 s.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell