Questions from General Calculus

Q: (a). How do you find the distance from a point

(a). How do you find the distance from a point to a line? (b). How do you find the distance from a point to a plane? (c). How do you find the distance between two lines?

Q: What are the traces of a surface? How do you find

What are the traces of a surface? How do you find them?

Q: A spring has natural length 0.75 m and a 5

A spring has natural length 0.75 m and a 5-kg mass. A force of 25 N is needed to keep the spring stretched to a length of 1 m. If the spring is stretched to a length of 1.1 m and then released with ve...

Q: Use power series to solve the differential equation. y' =

Use power series to solve the differential equation. y' = xy

Q: A spring with a mass of 2 kg has damping constant 14

A spring with a mass of 2 kg has damping constant 14, and a force of 6 N is required to keep the spring stretched 0.5 m beyond its natural length. The spring is stretched 1 m beyond its natural length...

Q: Verify that the Divergence Theorem is true for the vector field F

Verify that the Divergence Theorem is true for the vector field F on the region E. F (x, y, z) = 〈x2, 2y, z〉, E is the solid cylinder y2 + z2 < 9, 0 < x < 2

Q: Solve the differential equation. y'' - 2y' + 10y =

Solve the differential equation. y'' - 2y' + 10y = 0

Q: Use Stokes’ Theorem to evaluate ∫∫S curl F  dS.

Use Stokes’ Theorem to evaluate ∫∫S curl F  dS. F (x, y, z) = xyz i + xy j + x2yz k, S consists of the top and the four sides (but not the bottom) of the cube with vertices (±1, ±1, ±1), oriented out...

Q: Identify the surface with the given vector equation. r (

Identify the surface with the given vector equation. r (s, t) =〈3 cos t, s, sin t〉, -1 < s < 1

Q: A spring has a mass of 1 kg and its spring constant

A spring has a mass of 1 kg and its spring constant is k = 100. The spring is released at a point 0.1 m above its equilibrium position. Graph the position function for the following values of the damp...