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Hyperbola of one/two sheets and cone
Transitions of quadric surfaces
Hyperbolic paraboloid - as in Section 12.6
Level curves for \(f(x,y) = \dfrac{1}{\sqrt{1-x^2-y^2}}\)
Level curves for \(f(x,y) = \sqrt{x^2+y^2}\)
Level surfaces for \(f(x,y) = x^2 + y^2 - z^2\)
A function that has no limit at (0, 0) but the limit exists along all traces through (0, 0)
Partial derivatives and tangent plane
A function that is non-differentiable at (0, 0) but all traces through (0, 0) are differentiable
Directional derivative and the gradient vector
Critical points of a differentiable function
Absolute maxima and minima of a continuous function in a closed and bounded region
Absolute extrema of a function subject to a constraint (2 variables)
Absolute extrema of a function subject to a constraint (3 variables)
Absolute extreme of a function subject to two constaints (3 variables)
Integration limits of a triple integral
A point in spherical coordinates
A box in spherical coordinates
By Joseph Lo, CWSEI, Department of Mathematics, University of British Columbia