Questions from General Calculus

Q: Find a vector function that represents the curve of intersection of the

Find a vector function that represents the curve of intersection of the two surfaces. The cylinder x2 + y2 = 4 and the surface z = xy

Q: Find a vector equation for the tangent line to the curve of

Find a vector equation for the tangent line to the curve of intersection of the cylinders x2 + y2 = 25 and y2 + z2 = 20 at the point (3, 4, 2).

Q: Find a vector function that represents the curve of intersection of the

Find a vector function that represents the curve of intersection of the two surfaces. The paraboloid z = 4x2 + y2 and the parabolic cylinder y = x2

Q: Find a vector function that represents the curve of intersection of the

Find a vector function that represents the curve of intersection of the two surfaces. The hyperboloid z = x2 - y2 and the cylinder x2 + y2 = 1

Q: Find a vector function that represents the curve of intersection of the

Find a vector function that represents the curve of intersection of the two surfaces. The semiellipsoid x2 + y2 + 4z2 = 4, y > 0, and the cylinder x2 + z2 = 1

Q: Try to sketch by hand the curve of intersection of the circular

Try to sketch by hand the curve of intersection of the circular cylinder x2 + y2 = 4 and the parabolic cylinder z = x2. Then find parametric equations for this curve and use these equations and a comp...

Q: If two objects travel through space along two different curves, it’s

If two objects travel through space along two different curves, it’s often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft colli...

Q: Two particles travel along the space curves /

Two particles travel along the space curves Do the particles collide? Do their paths intersect?

Q: (a). Graph the curve with parametric equations /

(a). Graph the curve with parametric equations (b). Show that the curve lies on the hyperboloid of one sheet 144x2 + 144y2 - 25z2 = 100.

Q: Suppose u and v are vector functions that possess limits as t

Suppose u and v are vector functions that possess limits as t → a and let c be a constant. Prove the following properties of limits.