Therefore, T3(x) = and the graph of the functions f and T3 is below. 2 Find...
(1 point) Find the degree 3 Taylor polynomial T3(x) centered at a = 4 of the function f(x) = (-5x + 24)312]. T3(x) = ? ✓ The function f(x) = (-5x + 24)32) equals its third degree Taylor polynomial T3 (x)/centered at a = 4l. Hint: Graph both of them. If it looks like they are equal, then do the algebra.
2. Find the Taylor polynomial of degree 3 (T3(x)) for each of the following functions with the specified center: (a) f(x) = er at a = 1 (b) f(x) = cos(2.r) at a = ? (c) f(x) = x2 + e + at a = -1
Find the degree 3 Taylor polynomial T3(x) of the function f(x)=(7x+50)4/3 at a=2Find the second-degree Taylor polynomial for f(x)=4x2−7x+6 about x=0thank you! (:
please find the correct answer Find the Taylor polynomial T3(x) for the function f centered at the number a. Fle) = long a- T3(x) = 2(x - 1) - 12(x - 1)2 + 170 (x - 1)
[2 marks] Using the Taylor Remainder Theorem, what is the upper bound on f(x) – T3(x)], for x E [2, 10] if f(x) = 3 cos x and T3(x) is the Taylor polynomial centered on 6. SH
2. (a) (4 points) Find the Taylor polynomial T3(x) for the function f(z) = zez about a = 1, Please, do NOT use notation, you have to write all terms of Ts and they have to be simplified. b) (4 points) Use the Taylor's inequality to estimate the accuracy of the approximation f(x)T3(x) for くバ, (Do NOT give decimal fractions as your answer, Do NOT use a calculator leave your answer as an algebraic expression.) 2. (a) (4 points) Find...
1a. Find the equation y-f(x)-f'(x.)*(x-%) of a tangent line to the graph of a polynomial function f(x) -2xN4-x+3 3x^*2 at the point x, -1. (See the files Derivatives.doc and Derivatives of a power function.doc) N-16 1 b. Find the equation y-f(xi)-f'(x.)*(x-%) tangent line to the graph of a function of a f(x)-4x atx, 2. (Use the chain rule of differentiation for finding f'(x,).)
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)...
Consider the following function f (r) In(1 2r),a -5, n-3,4.6S 5.4 (a) Approximate f by a Taylor polynomial with degree n at the number a T3(x)- (b) Use Taylor's Inequality to estimate the accuracy of the approximation f Tn(x) when x lies in the given interval. (Round the answer to six decimal places.) R3(x)l S (c) Check your result in part (b) by graphing Rn(x). (Do this on your graphing device. Your instructor may ask to see this graph.) Need...
2. Graph the functions f(x)x(x 1)(x-2) ..(x- k) for k- 1,2,..,10. (These are examples of the polynomials occurring in the error formula for polynomial interpolation.) We want to produce an evenly spaced table of values for the function f(x) sin(x) for x E [O,T/2] such that, with cubic interpolation, we can give the values of the function at any point in the interval with an error less than 5 10-12. That means finding a number n such that with h-/2n...