Learn how points, direction vectors, and normal vectors build lines and planes in three dimensions. Work through equations, intersections, distances, and tangent-plane normals with 10 visual slides and 12 practice problems with solutions.
Partial derivatives measure how a multivariable function changes when one input varies and the others are held constant. This complete Calculus 3 lesson develops limit definitions, trace curves, first and mixed partials, tangent planes, the multivariable chain rule, linear approximation, rigorous counterexamples, and solved practice problems.