MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 13.2 Fa 2014

2. For the function f(x, y, z) = 2x2 + 3y-z points each Find f (1,-2,1) Find f(-2,1,0) What is the domain of f(x, y) = cos-1(x2 + y2)? 3, what is the domain of the function f(x))=Jr-2x ? Please ints shade in the region in the x-y plane that represents the domain

Suppose that a function f(x, y, z) is differentiated the point (0, -1, -2) and L(x, y, z) = x + 2y is the local linear approximation to f Find f(0, -1, -2), fx(0, -1, -2) fy(0, -1, -2) fz(0, -1, -2). A function f is given along with a local linear approximation L to f at a point P. Use the information given by determine point P. f(x, y) = x2 + y2; L(x, y) = 2y - 2x - 2 f(x, y) = x2y; L(x, y) = 4y - 4x + 8 f(x, y, z) = xy + z2; L(x, y, z) = y + 2x - 1 f(x, y, z) = xyz; L(x, y, z) = x - y - z - 2 The length and width of a rectangle are measured with of at most 3% and 5%, respectively. Use differentials to approximate the maximum percentage error in the calculated area.

2-6 Use Stokes' Theorem to evaluate is curl F dS. 2. F(x, y, z) = x2 sin z i + y 2 j + xy k, y that lies S is the part of the paraboloid z1 above the xy-plane, oriented upward 3, F(x, y, z) ze i + x cos y j + xz sin y k, S is the hemisphere x2 + y2 + z2 = 16, y the direction of the positive y-axis 0, oriented in 4. F(x, y, z) tan-i (xyz?) i + x2yj + x":-k, S is the cone x-v/y2 + Z2, 0 direction of the positive x-axis 2, oriented in the 5, F(x, y, z) = xyz i + xy j + x2yz k, S consists of the top and the four sides (but not the bottom) of the cube with vertices (+1, +1, t1), oriented outward 6. F(x, y, z) = e"i + ex: j + x": k, S is the half of the ellipsoid 4x2 y +4z2 4 that lies to the right of the xz-plane, oriented in the direction of the positive y-axis 7-10 Use Stokes' Theorem to evaluate c F dr. In each case is oriented counterclockwise as viewed from above. 7. F(x, y, z) = (x + y*) i + (y + z?) j + (z + x*) k, C is the triangle with vertices (1,00 0