Multivariable Calculus TOP Exam Questions And CORRECT Answers
Distance between two points (a,b,c) and (x,y,z)d = sqrt((x-a)^2 + (y-b)^2 + (z-c)^2) cross sections vs level curvescross sections: vertical slices of the graph of f(x,y) formed using vertical planes x=c (f(c,y)=z) or y=c (f(x,c)=z). Level curves: horizontal slices of f(x,y) using horizontal planes z=c (f(x,y) =c). Both used to plot graphs of functions with multiple variables. contour diagramsa family of graphs of the equation f(x,y) = c plotted in the xy-plane, for set values of c, usually labeled by the values. Values of c usually plotted in equal increments. (like topographical map) m and nm= slope in positive x direction dz/dx (holding y constant) n = slope in positive y direction dz/dy (holding x constant) equation for plane passing through the point (x0, y0, z0) with slope m in +x direction and n in +y directionz-z0 = m(x-x0) + n(y-y0) Point-slope: f(x,y) = z = z0 + m(x-x0) + n(y-y0)
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