Questions from General Calculus

Q: If p(x) is the total value of the production

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is A(x) = p(x) / x (a) Find A’(x). Why does the company wa...

Q: Prove the property of cross products (Theorem 11). Property

Prove the property of cross products (Theorem 11). Property 2: (ca) × b = c (a × b) = a × (cb)

Q: Prove the property of cross products (Theorem 11). Property

Prove the property of cross products (Theorem 11). Property 3: a × (b + c) = a × b + a × c

Q: Find the area of the parallelogram with vertices P (1,

Find the area of the parallelogram with vertices P (1, 0, 2), Q (3, 3, 3d), R (7, 5, 8), and S (5, 2, 7).

Q: Suppose y = f (x) is a curve that always

Suppose y = f (x) is a curve that always lies above the x-axis and never has a horizontal tangent, where f is differentiable everywhere. For what value of y is the rate of change of y5 with respect to...

Q: Find dy/dx by implicit differentiation. y cos x

Find dy/dx by implicit differentiation. y cos x = x2 + y2

Q: Find the cross product a × b and verify that it is

Find the cross product a × b and verify that it is orthogonal to both a and b. a = 2j - 4k, b = 2i + 3j + k

Q: (a) Find a nonzero vector orthogonal to the plane through

(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and (b) find the area of triangle PQR. P (0, 0, -3), Q (4, 2, 0), R (3, 3, 1)

Q: (a) Find a nonzero vector orthogonal to the plane through

(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and (b) find the area of triangle PQR. P (0, -2, 0), Q (4, 1, -2), R (5, 3, 1)

Q: (a) Find a nonzero vector orthogonal to the plane through

(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and (b) find the area of triangle PQR. P (2, -3, 4), Q (-1, -2, 2), R (3, 1, -3)