Section 4.2 « Difference Equations to Differential Equations

Section 4.2

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1. (a) $A_T = \dfrac{11}{32}$ , $A_M = \dfrac{21}{64}$

(c) $A_T = \dfrac{101}{60}$ , $A_M = \dfrac{496}{315}$

(e) $A_T = 30$ , $A_M = 29$

2. (a) $A_S = \dfrac{1}{3}$

(c) $A_S = \dfrac{6089}{3780}$

(e) $A_S = \dfrac{88}{3}$

3. (a) $A_T = 0.33340$ , $A_M = 0.33330$

(c) $A_T = 166.92480$ , $A_M = 166.78760$

(e) $A_T = -6.28525$ , $A_M = -6.28215$

(g) $A_T = 2.74670$ , $A_M = 2.74685$

4. (a) $A_S = 0.33333$

(c) $A_S = 166.83333$

(e) $A_S = -6.28318$

(g) $A_S = 2.74680$

5. (a) Stop when $n = 4$ , $A_S = 21$

(c) Stop when $n = 4$ , $A_S = 1.57080$

(e) Stop when $n = 32$ , $A_S = 7.64040$

8. (a) $A_S = 428$

(b) $A$ represents the average temperature over that $12$ hour period.

(c) Rounded to two decimal places, $A = 35.67$ and

$\displaystyle{\frac{1}{25}\sum_{t=0}^{24} T\left(\frac{t}{2}\right) = 36.04.}$

9. Area $\displaystyle{= \int_0^\pi \sin^2(x)dx = 1.57080}$ , rounded to five decimal places.

10. Area $\displaystyle{= \int_0^1 x^2dx + \int_1^2 (x - 2)^2dx = 0.66667}$ , rounded to five decimal places.

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