Exercises

1.
Define the functions f (x) = x3 + x sin x and g(x) = sin x2. Evaluate f (g(x)), g(f (x)), f (x)g(x), and f (x) + g(x).BITMAPSETAnswer0.2171in0.2006in0ina1

2.
At Metropolis Airport, an airplane is required to be at an altitude of at least 800 $\unit$ft above ground when it has attained a horizontal distance of 1 $\unit$mi from takeoff. What must be the (minimum) average angle of ascent?BITMAPSETAnswer0.2171in0.2006in0ina2

1.
Experiment with expansions of sin nx in terms of sin x and cos x for n = 1, 2, 3, 4, 5, 6 and make a conjecture about the form of the general expansion of sin nx.BITMAPSETAnswer0.2214in0.205in0ina3

2.
Experiment with parametric plots of $\left(\vphantom{ \cos t,\sin t}\right.$cos t, sin t$\left.\vphantom{ \cos t,\sin t}\right)$ and (t, sin t). Attach the point $\left(\vphantom{ \cos 1,\sin 1}\right.$cos 1, sin 1$\left.\vphantom{ \cos 1,\sin 1}\right)$ to the first plot and $\left(\vphantom{ 1,\sin 1}\right.$1, sin 1$\left.\vphantom{ 1,\sin 1}\right)$ to the second. Explain how the two graphs are related.BITMAPSETAnswer0.2214in0.205in0ina4

3.
Experiment with parametric plots of $\left(\vphantom{ \cos t,\sin t}\right.$cos t, sin t$\left.\vphantom{ \cos t,\sin t}\right)$, $\left(\vphantom{ \cos t,t}\right.$cos t, t$\left.\vphantom{ \cos t,t}\right)$, and $\left(\vphantom{ t,\cos t}\right.$t, cos t$\left.\vphantom{ t,\cos t}\right)$, together with the point $\left(\vphantom{ \cos 1,\sin 1}\right.$cos 1, sin 1$\left.\vphantom{ \cos 1,\sin 1}\right)$ on the first plot, $\left(\vphantom{ \cos 1,1}\right.$cos 1, 1$\left.\vphantom{ \cos 1,1}\right)$ on the second, and $\left(\vphantom{ 1,\cos 1}\right.$1, cos 1$\left.\vphantom{ 1,\cos 1}\right)$ on the third. Explain how these plots are related.BITMAPSETAnswer0.2214in0.205in0ina5