The divided difference table above is for the data:f(x)-0.29(7)0.00.10.70280 0.13534 -0.14943a) Do not apply any rounding.0.5a₁-1.15180.7For the second degree polynomial, P₂(x), with starting node x₁ = 0.7, obtained with the divideddifference method (by reading the divided difference table from the downside up), and thatpasses through the points (0.1,-0.14943), (0.5, -1.1518) and (0.7,-1.4845), the coefficientsare:14845a(2)11

The divided difference table is used to determine the interpolating polynomial using the divided…

Answered: The divided difference table above is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(B) For the following data in table: 50 618 x /(x) Find f(160) by using: L 11. III. 100 724 150 805 First order Interpolation (Direct Method). Second order interpolation (Lagrange Method). Appropriate central difference formula. 200 906 250 1032
The heat index (HI) is an estimate of the temperature felt by the human body based on the actual measured air temperature T (in °F) and relative humidity h,. It is given by HI = - 42.379 + 2.049015237 + 10.14333127h, – 0.22475541Th, – (6.83783 × 10-³)T² - (5.481717 x 10-3)h,² + (1.22874 × 10-³)7°h, + (8.5282 - 10-4)Th,² - (1.99 x 10-")T®h,?. a. If the air temperature in your area is 107°F with a relative humidity of 8%, how hot does your body feel? b. If the air temperature and relative humidity is known to be increasing at a rate of 2°F per sec and 1% per sec, resp., how fast is the heat index changing at the moment when the air temperature in your area is 107°F with a relative humidity of 8%?
Find the expression of Px²9x²(x +t), pxμ(x + t) with steps, if s(x +t) = s(x)(1-t) s(x + 1)t (Exponential Interpolation Assumption of Fractional Ages)
Q2) (a) Determine the roots of f (x) = -6+ 10.5x +9x2- 1.375x graphically. In addition, determine the final root of the function using (b) bisection and (c) false position for (b) and (c) use initial guesses of x = -1 and O and a stopped criterion of 40%.
Consider the experimental data below from a chemical reaction. xi | 1.435 | 2.235 | 3.035 f(xi) |4.35 |2.97 | 2.2 (a) Construct a divided difference table of the data and approximate f(2.5) using the Newton’s second degree (10) interpolating polynomial. Explain the comparison of this and the answer in (a) above.
The polynomial regression model of degree r is given by Y₁ =B₁ + B₁X₁ + ³₂X² + ... + ß₂X{ + U₁. The estimated cubic regression function relating income to test scores is Test Score = 600.1+5.02 Income -0.096Income² +0.00069 Income³. (5.1) (0.71) (0.029) (0.00035) The values in parenthesis are the standard errors of coefficient esti- mates. Test the null hypothesis that the regression function is quadratic against the alternative that it is cubic.
Suppose you have four data points xo ... x4 as shown on the figure to the right. Note that the data are not evenly spaced. We desire f(x) to estimate the value of f(x*). 6. On the figure, DRAW what a polynomial regression of order zero would look like. Label the line as "A. 7. On the figure, DRAW what a polynomial regression of order one would look like. Label the line as "B." 8. In the space below, write the regression equation for the polynomial you would choose to estimate the value of f(x*). Leave all coefficients as unknowns. Then, DRAW how it should look on the figure. Label is as line "C." O Xo X1 x* O + x X2 X3
In calculus, certain functions can be approximated by polynomial functions. Explore one such function now. Answer parts (a) through (d). (a) Using a graphing utility, create a table of values with Y₁ = f(x) = 1 1-x - 1

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