MAT 203 Final: MAT 203 Final Exam Review 203-s09

• School: Stony Brook University
• Department: Mathematics
• Course: MAT 203
• Professor: All

Document Summary

Review for mat 203 final exam (1) set f (x, y) = yln(y) + xy2, u = 2 1/2i + 2 1/2j and v = 2 131/2i + 2 1j. (a) compute the directional derivatives duf (1, 2) and dvf (1, 2). Solution: using 13. 10 on page 934 we get that. Duf (1, 2) =< 4, 5 + ln(2) > < 2 1/2, 2 1/2 >= (ln(2) + 9)/21/2. Solution: w = grad(f )(1, 2)/ k grad(f )(1, 2) k (see 13. 11 on page. 935). (2) find an equation for the tangent plane to the surface given by z2 +3x2 y2 = 3 at the point (0, 1, 2). Solution: set f (x, y, z) = z2 + 3x2 y2; the vector grad(f )(0, 1, 2) = 2j + 4k is the normal direction to the tangent plane. Thus an equation for the tangent plane is.