Questions from College Mathematics

Q: Find each indefinite integral and check the result by differentiating.

Find each indefinite integral and check the result by differentiating.

Q: Let F(x, y) = 5x - 4y +

Let F(x, y) = 5x - 4y + 12. Find all values of x such that F(x, 0) = 0.

Q: Let F(x, y) = xy + 2x2 +

Let F(x, y) = xy + 2x2 + y2 - 25. Find all values of y such that F(y, y) = 0.

Q: Let G(a, b, c) = a3 +

Let G(a, b, c) = a3 + b3 + c3 – (ab + ac + bc) - 6. Find all values of b such that G(2, b, 1) = 0.

Q: For the function ((x, y) = x2 + 2y2

For the function ((x, y) = x2 + 2y2 , find

Q: For the function ((x, y) = 2xy2 , find

For the function ((x, y) = 2xy2 , find

Q: Find the coordinates of B and H in the figure for Matched

Find the coordinates of B and H in the figure for Matched Problem 6 on page 807.

Q: Let ((x, y) = √4 - y2 .

Let ((x, y) = √4 - y2 . (A) Explain why the cross sections of the surface z = ((x, y) produced by cutting it with planes parallel to x = 0 are semicircles of radius 2. (B) Describe the cross section...

Q: Let ((x, y) = 100 + 10x + 25y

Let ((x, y) = 100 + 10x + 25y - x2 - 5y2 . (A) Describe the cross sections of the surface z = ((x, y) produced by cutting it with the planes y = 0, y = 1, y = 2, and y = 3. (B) Describe the cross se...

Q: Let f1x, y2 = 4 - √x2 + y2 .

Let f1x, y2 = 4 - √x2 + y2 . (A) Explain why f1a, b2 = f1c, d2 whenever 1a, b2 and 1c, d2 are points on the same circle with center at the origin in the xy plane. (B) Describe the cross sections of...