finally,
The forward difference formula is better for error approximation than Taylor's formula.
03) Use the following rules with the indicated values of x to approximate the given function...
Consider the following function #x)-x2/5, a-1, n-3, 0.7 sxs 1.3 (a) Approximate fby a Taylor polynomial with degree n at the number a T3(x) (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) Tn(x) when x lies in the given interval. (Round your answer to eight decimal places.)
Consider the following function #x)-x2/5, a-1, n-3, 0.7 sxs 1.3 (a) Approximate fby a Taylor polynomial with degree n at the number a T3(x) (b) Use Taylor's Inequality to...
Question 4 (16 Points) Use Neville's method to approximate V11 with the following function and values. Use this polynomial to approximate f(11). Using 4-digit rounding arithmatic. (a). f(x) = (x and the values Xo = 6, xı = 8, x2 = 10, x3 = 12 and X4 = 13. (b). Compare the accuracy of the approximation in parts (a).
Consider the following function. /(x)=x-5, a= 1, n= 2, 0.8SXS 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a T2(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) ~ Tn(x) when x lies in the given interval. (Round your answer to six decimal places.) (c) Check your result in part (b) by graphing Rn(x) 0.6 0.4 0.2 0.6 0.4 0.2 0.9 0.9 1.2 -0.2 -0.4 -0.6 -0.2 -0.4 -0.6...
Consider the following function. (x) = x-8, (a) Approximate fby a Taylor polynomial with degree n at the number a. 0.8 s xs 1.2 n=2, a31, T2(x) = Tmx) when x lies in the given interval. (Round your answer to six decimal places.) (b) Use Taylor's Inequality to estimate the accuracy of the approximation rx (c) Check your result in part (b) by graphing R(x)l 3 2.5 2.0 1.2 WebAssign Plot 0.9 0.5 1.2 0.9 3 1.2 1.0 -0.5 1.0...
3. Approximate the function f(x) = Vx by T4(x), the Taylor polynomial of degree 4 centred at x = 1. Do this in two ways: (a) Use the general formula at the top of page 60--calculating successive derivatives of vx. (b) Change variable so you can directly use the formula of Ex 4.6: 1 17 1/ 11315 (1 + y)1/2 = 1+3y + 2 + - 41 2 y4 + ... ull- 2 2 2 Now we ask how accurate...
Consider the following function. f(x) = 5 sinh (3r). a = 0, n=5,-0.3<r <0.3 (a) Approximate f by a Taylor polynomial with degree n at the number a. 3 45x 2 81 5 T5(x) = | 15x + + -X 8 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f = 7,(x) when x lies in the given interval. (Round the answer to four decimal places.) |R5(x)] = 5.19674 X
Consider the following function rx)=x sin(x), a=0, n= 4, -0.9 0.9 x (a) Approximate fby a Taylor polynomial with degree n at the number a (b) Use Taylor's Inequality to estimate the accuracy of the approximation rx)俗,(x) when x lies in the given interval. (Round M up to the nearest integer. Round your answer to four decimal places.) R4X) 0.00453X (c) Check your result in part (b) by graphing Rn(x)| 0.5 -0.5 -0.001 -0.002 002 0.003 -0.003 0.004 -0.004 0.005...
question b please
Consider the following function f(x) -x6/7, a-1, n-3, 0.7 sx 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a 343 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ,(x) when x lies in the given interval. (Round your answer to eight decimal places.) IR3(x)0.00031049 (c) Check your result in part (b) by graphing Rn(x)l 2 1.3 0.00015 0 0.9 1.0 11 -0.00005 0.00010 -0.00010 0.00005 0.00015 0.8...
Consider the function φ (x,y)-ex + e". Consider the point (x,y)= (1,1). Dyalculate the exact values ofipor and 0φ。y at this point b) Ue first-order forward differences, with Ax Ay 0., to calculate approximate valueoföx and öpy at point (1, 1). Calculate the percentage difference when compared with the exact values from part (a). (c) Use first-order rearward differences, with Ar = 0.1, to calculate approximate values of 6fax and öply at point (1, Ealculate the percentage difference when mpared...
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14. 514 points | Previous Answers SCal:ET 11.11.021. Consider the following function. /(x) = x sin(x), a = 0, n = 4, -0.9 x 0.9 (a) Approximate fby a Taylor polynomial with degree n at the number a (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) * Tp(x) when x lies in the given interval. (Round M up to the nearest integer. Round your answer...