Graphing Solutions of Differential Equations, #6: Graphs

Graphing Solutions to Differential Equations, # 20: Graphs

Numerical Solutions, #4: Decreasing

Numerical Solutions, #8: $5.90625$

Numerical Solutions, #12: (a) $f' = k f$ for some constant $k$, $f(0) = 2$, (b) $f(1) \approx 2 + \frac{5}{2} k$, (c) $f(t) = 2 e^{kt}$, (d) if $k = 0.3$, then $f(1) = 2 e^{-0.3} \approx 1.48$ while the approximation from (b) gives $f(1) \approx 2 + \frac{5}{2} (-0.3 = 1.25$.

Numerical Solutions, #20: (a) E, (b) C, (c) D, (d) A, (e) B

11.1, # 4: $-1 + \frac{25}{2} x^2$

11.1, # 8: $1 - \frac{1}{2} x + \frac{3}{8} x^2 - \frac{5}{16} x^3$

11.1, # 22: $-0.22$

11.1, # 26: $f''(1) = 3$, $f'''(1) = -5$