Questions from General Calculus

Q: (a). Find the arc length function for the curve measured

(a). Find the arc length function for the curve measured from the point P in the direction of increasing t and then reparametrize the curve with respect to arc length starting from P, and (b). find t...

Q: (a). Find the arc length function for the curve measured

(a). Find the arc length function for the curve measured from the point P in the direction of increasing t and then reparametrize the curve with respect to arc length starting from P, and (b). find t...

Q: Match the parametric equations with the graphs (labeled I–VI

Match the parametric equations with the graphs (labeled I–VI). Give reasons for your choices. x = t cos t, y = t, z = t sin t, t > 0

Q: Match the parametric equations with the graphs (labeled I–VI

Match the parametric equations with the graphs (labeled I–VI). Give reasons for your choices. x = cos t, y = sin t, z = 1/ (1 + t2)

Q: Match the parametric equations with the graphs (labeled I–VI

Match the parametric equations with the graphs (labeled I–VI). Give reasons for your choices. x = t, y = 1 / (1 + t2), z = t2

Q: Match the parametric equations with the graphs (labeled I–VI

Match the parametric equations with the graphs (labeled I–VI). Give reasons for your choices. x = cos t, y = sin t, z = cos 2t

Q: Match the parametric equations with the graphs (labeled I–VI

Match the parametric equations with the graphs (labeled I–VI). Give reasons for your choices. x = cos 8t, y = sin 8t, z = e0.8t, t > 0

Q: Match the parametric equations with the graphs (labeled I–VI

Match the parametric equations with the graphs (labeled I–VI). Give reasons for your choices. x = cos2 t, y = sin2 t, z = t

Q: Show that the curve with parametric equations x = t cos t

Show that the curve with parametric equations x = t cos t, y = t sin t, z = t lies on the cone z2 = x2 + y2, and use this fact to help sketch the curve.

Q: Show that the curve with parametric equations x = sin t,

Show that the curve with parametric equations x = sin t, y = cos t, z = sin2t is the curve of intersection of the surfaces z = x2 and x2 + y2 = 1. Use this fact to help sketch the curve.