Find the slope of the line tangent to the surface z = 3x2 + 4xy + y2 - 3x - 4y + 2, passing through the given point (2, -1, 5), and parallel to the xz - plane. -4 6 2 5 Find the total differential of function z =4x2 - 8xy - 3y2 dz = (8x + 8y)dx - (8x + 6y)dy dz = (8x - 8y)dx + (8x + 6y)dy dz = (8x - 6y)dx - (8x + 8y)dy dz = (8x - 8y)dx - (8x + 6y)dy Find the total differential function z = In(x2 + y2) 2x / x2 + y2 dx - 2y / x2 + y2 dy - 2x / x2 + y2 dx = 2y / x2 + y2 dy 2y / x2 + y2 dx + 2x / x2 + y2 dy - 2x / x2 + y2 dx + 2y / x2 + y2 dy The sum of three numbers is 40 and their product is a maximum. Find the value of the three numbers. (40 / 3, 40 / 3, -40 / 3) (0, 0, 40) (40 / 3, 40 / 3, 40 / 3) (0, 40, 0) Solution 10. 11.A 12.D 13.C.

1. Find the slope of the line tangent to the surface z = 3x2 + 4xy + y2 - 3x - 4y + 2, passing
through the given point (2, -1, 5), and parallel to the xz - plane. -4 6 2 5 Find the total
differential of function z =4x2 - 8xy - 3y2 dz = (8x + 8y)dx - (8x + 6y)dy dz = (8x - 8y)dx + (8x
+ 6y)dy dz = (8x - 6y)dx - (8x + 8y)dy dz = (8x - 8y)dx - (8x + 6y)dy Find the total differential
function z = In(x2 + y2) 2x / x2 + y2 dx - 2y / x2 + y2 dy - 2x / x2 + y2 dx = 2y / x2 + y2 dy
2y / x2 + y2 dx + 2x / x2 + y2 dy - 2x / x2 + y2 dx + 2y / x2 + y2 dy The sum of three numbers
is 40 and their product is a maximum. Find the value of the three numbers. (40 / 3, 40 / 3, -40 /
3) (0, 0, 40) (40 / 3, 40 / 3, 40 / 3) (0, 40, 0)
Solution
10. 11.A 12.D 13.C