Section 3.6 « Difference Equations to Differential Equations

Section 3.6

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1. (a) Three solutions: $-2.3407$ , $-0.9018$ , $2.4080$

(e) Two solutions $0.7135$ , $2.0730$

2. (d) If $\displaystyle{L = \lim_{n \to \infty}x_n}$ , then
$\displaystyle{L = \lim_{n \to \infty}x_{n+1} = \lim_{n \to \infty}\frac{x_n + \dfrac{c}{x_n}}{2} = \frac{L + \dfrac{c}{L}}{2}}$ ,
from which it follows that $L^2 = c$ .

3. $1.25992$

4. $1.25850$

6. The values oscillate between $1$ and $-1$ ; that is, for $n = 0, 1, 2, \ldots$ , $x_{2n} = 1$ and $x_{2n + 1} = -1$ .

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Difference Equations to Differential Equations

Section 3.6

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