Calculus 3: Linearization, chain rule, gradient
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All Calculus 33D SpaceVector FunctionsDot and cross productEquations of lines and planesParametric curves, conic sectionsTangent vectors and arc lengthCylinders and quadric surfacesIntegrals of vector functionsArc length and curvatureMultivariable functionsSurface parameterizationPartial derivativesLinearization, chain rule, gradientTangent planes and linear approximationsOptimizationLagrange multipliersDouble integralsTriple integralsChanging coordinates for integrationSurface areaVector fields, divergence, and curlLine integralsGreen's TheoremFluxStokes' TheoremDivergence TheoremComplex numbers
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Given the function , find the linearization of the function at the point .
The base radius and height of a right circular cone are 10 cm and 25 cm, with a possible error in measurement of as much as 0.1 cm in each. Use differentials to estimate the maximum error in the calculated volume of the cone.