If f(0)-o, f(0)-4, P'(0)-0, and f" (0)-2, then which of the following is the third-order Taylor...
Find the Taylor polynomials of order 0, 1, 2, and 3 generated by fat a. f(x)= Vx, a=4 The Taylor polynomial with order 0 is P(x)=
2. a) Find Ts(x), the third degree Taylor polynomial about x -0, for the function e2 b) Find a bound for the error in the interval [0, 1/2] 3. The following data is If all third order differences (not divided differences) are 2, determine the coefficient of x in P(x). prepared for a polynomial P of unknown degree P(x) 2 1 4 I need help with both. Thank you.
need help Determine the third Taylor polynomial at x = 0 for the function f(x)=34x+1. P3(x) = Determine the fourth Taylor polynomial of f(x) = at x = 0 and use it to estimate e 0.5 P(x)=0 Determine the fourth Taylor polynomial of 11 In x at x = 1. Pax)=0 41 The third remainder for f(x) at x = 0 is R, (x) where c is a number between 0 and x Let f(x) = cos x. (a) Find...
Find the third Taylor polynomial... (a) Find the third Taylor polynomial T,(x) for f(x)-x at a -1 (b.) Fill in the following table stating your answers to five decimal places T,(x) (from calculator) 2 4 4 (c.) Use Taylor's formula for Rn(x) to estimate the accuracy of the approximation Vr ~ T,(x) when x lies in the interval [T, . (a) Find the third Taylor polynomial T,(x) for f(x)-x at a -1 (b.) Fill in the following table stating your...
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)...
Question No.8 (a) Find the third-degree Taylor polynomial for f() = r3+7x2-5r1 about 0. What did you notice? (b) Use a calculator to calculate sin(0.1) cos(0.1). Now, using the second order Taylor polynomial, give an estimate for sin(0.1)+cos(0.1). Estimate the expression using the third-order Taylor polynomial, and compare the two approximations. Note that your estimates should be rounded to seven digits after the decimal place. same Question No.8 (a) Find the third-degree Taylor polynomial for f() = r3+7x2-5r1 about 0....
l. (Taylor Polynonial for cos(ar)) Fr f(z) = cos(ar) do the following. (a) Find the Taylor polynomials T.(r) about O 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 T(r) and TR+1(r)? (c) You might want to approximate cs(ar) for all x in。Ś π/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)-cos(2x). d)...
Let f(z-y2 sin(x+-) Answer the following. Show and explain your work. (a) Find the Taylor polynomial of order 4. generated by f(x) at zo (b) Describe the MacLaurin series of f (with or without the sigma notation). (Hint: What pattern do the derivatives of f at z-0 follow?) (c) Does the MacLaurin series of f converges absolutely, converges conditionally or diverges at -1? Let f(z-y2 sin(x+-) Answer the following. Show and explain your work. (a) Find the Taylor polynomial of...
For the function f(x) = e 2x, which of the following polynomials is the 2nd degree Taylor polynomial for f(2') at the point I = 0? 1) P(x) = 1-2+x2 2) P2 (3)=1-23 +22 3) P3(x) = 1 - 2.c + 2x2 4) P4(x) = 1 + 2x + 2x2 O Polynomial in 3) Polynomial in 1) O Polynomial in 2) O Polynomial in 4)
1. 2. 3. The function defined by f(x) = x4 + 4x3 - 16x2 - 64x has the graph, as shown. 200- X Use the graph to factor the polynomial. 7 -200 What is the factored form of the polynomial? f(x) = (Simplify your answer. Type your answer in factored form.) Graph the polynomial function f(x) = 2x3 X° + 1. Then answer parts a and b. Choose the correct graph below. O A. OB O c. OD У AY...