Find answers to the top 10 questions parents ask about TI graphing calculators.
Learn about the math and science behind what students are into, from art to fashion and more.
Get hundreds of video lessons that show how to graph parent functions and transformations.
Explore Taylor polynomials graphically and analytically, as well as graphically determine the interval where the Taylor polynomial approximates the function it models.
In this problem, students investigate a Taylor polynomial centered at zero.
Students will recall that this Taylor polynomial is also known as a Maclaurin polynomial. Students find the 4th degree Taylor polynomial that approximates f(x) = ln(x + 5) at x = 0. They will notice that the values are closest at the center and become farther apart the further the x-values are from the center.
This problem also gives students the opportunity to explore different degrees of a Taylor polynomial. They use the Taylor command to find the respective polynomials and graph the function with each of the larger power polynomials in turn.
This will demonstrate that a Taylor polynomial will only approximate the function over a given interval, no matter how large the Taylor Polynomial is.
At the end of this activity, students will be able to find the first few terms of a Taylor series approximation to a function for any given value of x. They will also be able to graph a function and its Taylor polynomials of various degrees to show their convergence to a function.
© Copyright 1995-2023 Texas Instruments Incorporated. All rights reserved.