Question

2 Given $f(x) = \frac{1}{x}$ and $x_i = 1 + \frac{i}{20}$, $i = 0, 1, \dots, 20$. Note that $x_0 = 1$, $x_{20} = 2$. A. Write the formula of the piecewise polynomial $S(x)$ on the interval $[x_i, x_{i+1}]$ for $i = 0, 1, \dots, 19$. B. Use the error estimate theorem to show that $|f(x) - S(x)| \le \frac{1}{1600}$. C. Verify the error estimate with $x = 1.42$

          2 Given $f(x) = \frac{1}{x}$ and $x_i = 1 + \frac{i}{20}$, $i = 0, 1, \dots, 20$. Note that $x_0 = 1$, $x_{20} = 2$.
A. Write the formula of the piecewise polynomial $S(x)$ on the interval $[x_i, x_{i+1}]$ for $i = 0, 1, \dots, 19$.
B. Use the error estimate theorem to show that
$|f(x) - S(x)| \le \frac{1}{1600}$.
C. Verify the error estimate with $x = 1.42$

2 Given f(x) = (1)/(x) and xi = 1 + (i)/(20), i = 0, 1, …, 20. Note that x0 = 1, x20 = 2.
A. Write the formula of the piecewise polynomial S(x) on the interval [xi, xi+1] for i = 0, 1, …, 19.
B. Use the error estimate theorem to show that
|f(x) - S(x)| ≤(1)/(1600).
C. Verify the error estimate with x = 1.42

Added by Jacob S.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Samuel Goyette

Step 1

First, we need to find the formula for the piecewise polynomial S(x) on the interval B. We are given that Xi = 1 + i/20 for i = 0, 1, ..., 20. Note that X0 = 1 and X20 = 2A. To find the formula for S(x), we need to find the polynomial that passes through the Show more…

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Given f(x) = 1/x and Xi = 1 + i/20, i = 0, 1, ... , 20. Note that X0 = 1, X20 = 2A. Write the formula of the piecewise polynomial S(x) on the interval B. Use the error estimate theorem to show that |f(x) - S(x)| < 1/1600C. Verify the error estimate with x = 1.2. Given f = and = 1 + i/20, i = 0, 1, ... , 20. Note that g = 1, z20 = 2A. Write the formula of the piecewise polynomial S on the interval [+] for i = 0, 1, 19 B. Use the error estimate theorem to show that. C. Verify the error estimate with x = 1.42.