Questions from General Calculus

Q: Find three different surfaces that contain the curve r(td

Find three different surfaces that contain the curve r(td) = 2t i + et j + e2t k.

Q: Find three different surfaces that contain the curve r(t

Find three different surfaces that contain the curve r(t) = t2 i + ln t j + s(1/t) k.

Q: At what points does the curve r(t) = t

At what points does the curve r(t) = t i + (2t - t2) k intersect the paraboloid z = x2 + y2?

Q: Find parametric equations for the tangent line to the curve with the

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

Q: Find parametric equations for the tangent line to the curve with the

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = ln (t + 1), y = t cos 2t, z = 2t, (0, 0, 1)

Q: Find parametric equations for the tangent line to the curve with the

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e-t cos t, y = e-t sin t, z = e-t; (1, 0, 1)

Q: Graph the curve with parametric equations x = sin t, y

Graph the curve with parametric equations x = sin t, y = sin 2t, z = cos 4t. Explain its shape by graphing its projections onto the three coordinate planes.

Q: Graph the curve with parametric equations x = (1

Graph the curve with parametric equations x = (1 + cos 16t) cos t y = (1 + cos 16t) sin t z = 1 + cos 16t Explain the appearance of the graph by showing that it lies on a cone.

Q: Graph the curve with parametric equations / Explain

Graph the curve with parametric equations Explain the appearance of the graph by showing that it lies on a sphere.

Q: Show that the curve with parametric equations x = t2, y

Show that the curve with parametric equations x = t2, y = 1 - 3t, z = 1 + t3 passes through the points (1, 4, 0) and (9, -8, 28) but not through the point (4, 7, -6).