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Math 241
Practice questions
| Question | Answer |
|---|---|
| Find the equation of the tangent plane to the hyperboloid below at (xo, yo, zo). (Enter in xo as x_0, yo as y_0, and zo as z_0.) x2/a2 + y2/b2 – z2/c2 = 1 | 14.6 #50 WA11 |
| At what point on the paraboloid y = x2 + z2 is the tangent plane parallel to the plane 3x + 4y + 9z = 1? (Enter NONE if the answer does not exist in all the answer blanks.) | 14.6 #52 WA11 |
| Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 7x2 + 2y2 + 3z2 = 21 at the point (-1, 1, 2). (Enter your answer in terms of t.) | 14.6 #59 WA11 |
| Find the local maximum and minimum values and saddle point(s) of the function. f(x, y) = 9(x2 + y2)ey2 - x2 | 14.7 #15 WA11 |
| Use a graph and or level cures to estimate local max/min/saddle points. Then use calculus to solve f(x,y)=sinx + siny + sin(x+y)...0<x<2pi, 0<y<2pi | 14.7 #23 |
| 14.6 #54 | 14.6 #54 |
| Find the absolute maximum and minimum values of f on the set D. f(x, y) = 9 + xy - x - 2y, D is the closed triangular region with vertices (1, 0), (5, 0), and (1, 4) | 14.7 #30 WA12 |
| Find the points on the surface y2 = 1 + xz that are closest to the origin. (Enter your answers from smallest to largest y - value.) | 14.7 #42 WA12 |
| Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 7 | 14.7 #47 WA12 |
| Find the maximum volume of a rectangular box that is inscribed in a sphere of radius r. | 14.7 #45 WA12 |
| 14.8 #1 | 14.8 #1 |
| 14.8 #21 | 14.8 #21 |
| Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2 = 4 + xz | 14.8 #27 WA13 |
| Find the extreme values of f on the region described by the inequality. f(x,y) = 2x2 + 3y2 - 4x - 6, x2 + y2 ≤ 16 | 14.8 #18 WA 13 |
| Find the directions in which the directional derivative has a value of 1. f(x,y)= ye^-xy | m(i)+m15/8(j) |
| Find all points at which the direction of fastest change of the function f(x,y)=x^2+y^2-2x-4y is i+j | any point on the line y=x+1 |
| The normal line of surface S at point P is: | It is given by the gradient DelF(x,y,z). In symmetric equations: x-x0/Fx = y-y0/Fy = z-z0/Fz |
Created by:
reynol32