Section 3.1 « Difference Equations to Differential Equations

Section 3.1

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1. (b) $m = 1$

2. (a) $o(h)$

(b) $O(h)$

(d) $o(h)$

(e) $o(h)$

(f) Neither

3. (b) $R_T$ is $O(h)$ , but not $o(h)$ .

(d) $S$ is the best affine approximation to $f$ at $9$ .

(e) $\sqrt{10} \approx S(10) = \dfrac{19}{6} = 3.167$ to three decimal places, whereas $\sqrt{10}$ is exactly $3.162$ to three decimal places.

5. $T(x) = 4(x - 1) + 2$ , $f'(1) = 4$

7. $T(x) = x - 1$ , $f'(0) = 1$

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Difference Equations to Differential Equations

Section 3.1

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