Question 1 (20 Points) Find the second Taylor polynomial P2(x) for the function f(x) = ex...
Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about xo = 0. Using 4-digit rounding arithmatic. (a). Use P2(0.7) to approximate f(0.7). (b). Find the actual error. (c). Find a bound for the error |f(x) – P2(x) in using P2(x) to approximate f(x) on the interval [0, 1].
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2 + 14x – 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos X – X. (a). Approximate a root of f(x) using Fixed- point method accurate to within 10-2 . (b). Approximate a root of f(x) using Newton's method accurate to within 10-2. Find the second Taylor polynomial P2(x) for the function f(x) =...
Q#1: Find the third Taylor polynomial P3(x) for the function f(x) Xo = 0. Evaluate when x = 0.1. Compute the error bound. 1+* about
Question 3 ( 14 Points) (a). Use the numbers (called nodes) Xo = 2.0, x1 = 2.4, and x2 = 2.6 to find the second Lagrange interpolating polynomial for f(x) = sin(In x). Using 4-digit rounding arithmatic. (b). Use this polynomial to approximate f(1). Using 4-digit rounding arithmatic.
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between Tn (x) and TR+1()? (c) You might want to approximate cos(az) for all in 0 xS /2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a -2, i.e. f(x)...
6. Find the second Taylor Polynomial for f(x) = csc x ex- panded about Xo = -. Here are some facts you may find useful: f'(x) = – csc(x) cot(x) csc(x) = -1 sin(x) f"'(x) = csc(x)(1 + 2 cot? (x) cot(x) = sin()
Please show work 1.For the function f(x) = ln(x + 1) find the second Taylor polynomial P2(x) centered at c = 2. (9 points) 2. Use the Maclaurin series for arctan x to find a Maclaurin series for f(x). 3. Find the radius of convergence and the interval of convergence of the power series. We were unable to transcribe this imageWe were unable to transcribe this image
The nth-order Taylor polynomial for a function f(x) using the h notation is given as: Pa (x + h) = f(x) + f'(a)h + salt) 12 + () +...+ m (s) n." The remainder of the above nth-order Taylor polynomial is defined as: R( +h) = f(n+1)(C) +1 " hn+1, where c is in between x and c+h (n+1)! A student is using 4 terms in the Taylor series of f(x) = 1/x to approximate f(0.7) around x = 1....
Question 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2 for x3 - 7x2 + 14x - 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos x - x. (a). Approximate a root of f(x) using Fixed-point method accurate to within 10-2 (b). Approximate a root of f(x) using Newton's method accurate to within 10-2.