Calculus II, Spring 2016

Quiz 4

Apr 28, 2016

1. Find a tangent vector to the curve given by the intersection of the two surfaces xyz = 1 and x^{2} + 2y^{2} + 3z^{2} = 6 at the point (1, 1, 1).

2. Find absolute maxima and minima of f(x, y) = x^{2} +xy +y^{2} −6x+2 on the rectangular 0 ≤ x ≤ 5, −3 ≤ y ≤ 3.

3. Use the method of Lagrangian multiplier (only) to find the maximum and minimum value of f(x, y, z) = x − 2y + 5z on the sphere x^{2} + y^{2} + z^{2} = 30.

4. Use Taylor’s formula to find the quadratic approximation of f(x, y) = \frac{1}{1 − x − y} near the origin.

5. Let U = f(P, V, T) where P, V and T are subject to the constraint P V = nRT, n, R are constants. Find (\frac{∂U}{∂P} )_{V} and (\frac{∂U}{∂T} )_{V}

Calculus II, Spring 2016

Quiz 4

Apr 28, 2016

1. Find a tangent vector to the curve given by the intersection of the two surfaces xyz = 1 and x^{2} + 2y^{2} + 3z^{2} = 6 at the point (1, 1, 1).

2. Find absolute maxima and minima of f(x, y) = x^{2} +xy +y^{2} −6x+2 on the rectangular 0 ≤ x ≤ 5, −3 ≤ y ≤ 3.

3. Use the method of Lagrangian multiplier (only) to find the maximum and minimum value of f(x, y, z) = x − 2y + 5z on the sphere x^{2} + y^{2} + z^{2} = 30.

4. Use Taylor’s formula to find the quadratic approximation of f(x, y) = \frac{1}{1 − x − y} near the origin.

5. Let U = f(P, V, T) where P, V and T are subject to the constraint P V = nRT, n, R are constants. Find (\frac{∂U}{∂P} )_{V} and (\frac{∂U}{∂T} )_{V}