Questions from General Calculus

Q: Find the Jacobian of the transformation. x = peq,

Find the Jacobian of the transformation. x = peq, y = qep

Q: Use Lagrange multipliers to give an alternate solution to the indicated exercise

Use Lagrange multipliers to give an alternate solution to the indicated exercise in Section 14.7. Exercise 42 14.7 Exercise 42: Find the point on the plane x - 2y + 3z = 6 that is closest to the poi...

Q: Find the Jacobian of the transformation. x = uv,

Find the Jacobian of the transformation. x = uv, y = vw, z = wu

Q: Find the Jacobian of the transformation. x = u +

Find the Jacobian of the transformation. x = u + vw, y = v + wu, z = w + uv

Q: Identify the surface whose equation is given. ρ cos φ

Identify the surface whose equation is given. ρ cos φ = 1

Q: Identify the surface whose equation is given. ρ = cos

Identify the surface whose equation is given. ρ = cos φ

Q: Write the equation in spherical coordinates. (a). x2

Write the equation in spherical coordinates. (a). x2 + y2 + z2 = 9 (b). x2 - y2 - z2 = 1

Q: Find the image of the set S under the given transformation.

Find the image of the set S under the given transformation. S is the disk given by u2 + v2 < 1; x = au, y = bv

Q: Sketch the solid described by the given inequalities. ρ <

Sketch the solid described by the given inequalities. ρ < 1, 0 < φ < π/6, 0 < θ  < π

Q: Sketch the solid described by the given inequalities. 1 <

Sketch the solid described by the given inequalities. 1 < ρ < 2, π/2 < φ < π