This preview shows page 1. Sign up to view the full content.
Unformatted text preview: y 2 j. (b) 1/6 (c) 1/3 (d) 2/3. (a) 1/12 Solution: (b) 3 15. The equation of the tangent plane to the surface z = x2 y + y 2 at the point (1, 1, 2) is: (a) 2x + 3y - z = 2 (c) 2x + 3y - z = 3 (d) 2x + 3y - z = 4. (b) 2x - 3y - z = 3 Solution: (c) THIS IS THE END OF THE QUESTIONS. 4 Formula Sheet
Most of the formulas and theorems provided are stated without the conditions under which they apply. The notation used is the same as that used in lectures. Line Integrals
b (x, y, z) ds =
C a (x(t), y(t), z(t)) dx dt 2 + dy dt 2 + dz dt 2 dt. C F dr = F1 dx + F2 dy + F3 dz = Work done by F along C.
C Grad grad = = i+ j+ k. x y z is normal to the tangent plane of the surface (x, y, z) = k, (k a constant). If F is continuous and equal to for some , then F is a conservative field, is a potential function of F, and
C F dr is path-independent. Curl i curl F = F = x F1 j y F2 k z F3 If the domain of F is simply connected and F = 0 then F is conservative. Double integrals ov...
View Full Document