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- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_Variables/1.06%3A_Directional_Derivatives_and_the_Gradient/1.6E%3A_Exercises_for_Section_1.6This page includes exercises on directional derivatives and gradients for functions such as f(x,y)=5−2x2−12y2 and f(x,y)=y2cos(2x), evaluated at points like P(3,4). It a...This page includes exercises on directional derivatives and gradients for functions such as f(x,y)=5−2x2−12y2 and f(x,y)=y2cos(2x), evaluated at points like P(3,4). It also covers gradients in multiple dimensions, tangent planes, and normal lines, alongside problems related to temperature change and electric potential.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/02%3A_Multiple_Integration/2.06%3A_Triple_Integrals_in_Cylindrical_and_Spherical_Coordinates/2.6E%3A_ExercisesThis page presents exercises focused on evaluating triple integrals over solid regions in three-dimensional space, using cylindrical and spherical coordinates. It includes function transformations, co...This page presents exercises focused on evaluating triple integrals over solid regions in three-dimensional space, using cylindrical and spherical coordinates. It includes function transformations, computations of volumes for shapes like cylinders and cones, and integral evaluations, providing explicit examples and solutions. Additionally, the document emphasizes the conversion between coordinate systems and discusses the properties of continuous functions with symmetry.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.09%3A_Calculus_of_the_Hyperbolic_Functions/2.9E%3A_Exercises_for_Section_2.9This page presents exercises on hyperbolic functions, including their derivatives, integrals, and identities, alongside problems involving physical applications like falling bodies and catenary curves...This page presents exercises on hyperbolic functions, including their derivatives, integrals, and identities, alongside problems involving physical applications like falling bodies and catenary curves. It also includes guidance on proving expressions for inverse hyperbolic functions, with emphasis on verification and application. The content is provided by contributors from MIT and Harvey Mudd, is licensed under CC-BY-SA-NC 4.0, and is free to download.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_Variables/1.02%3A_Limits_and_Continuity/1.2E%3A_Exercises_for_Section_1.2This page covers limits and continuity of functions in multiple variables, analyzing two and three-variable limits and their dependence on paths. It identifies regions of continuity and discontinuity,...This page covers limits and continuity of functions in multiple variables, analyzing two and three-variable limits and their dependence on paths. It identifies regions of continuity and discontinuity, concluding that some limits do not exist while others are continuous at certain points. It highlights f(g(x,y)) and f(x,y)=x2−4y as examples, noting specific continuity conditions. Contributions come from Gilbert Strang and Jed Herman, with a CC-BY-SA-NC 4.0 license.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/06%3A_AppendicesContributors and Attributions Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download fo...Contributors and Attributions Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_Variables/1.04%3A_Tangent_Planes_and_Linear_Approximations/1.4E%3A_Exercises_for_Section_1.4This page includes exercises on mathematical concepts like surfaces, normal and tangent vectors, tangent planes, differentials, and differentiability. It covers calculating equations for tangent plane...This page includes exercises on mathematical concepts like surfaces, normal and tangent vectors, tangent planes, differentials, and differentiability. It covers calculating equations for tangent planes and normal lines, applying total differentials, and estimating geometric changes in shapes. A specific problem involves finding the tangent plane for the surface z=sin(x+y2) at a given point, with graphical representations provided. The content is available under a CC-BY-SA-NC 4.
