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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.10%3A_Chapter_3_Review_ExercisesThis page contains exercises on calculus derivatives, including evaluating derivatives, proving statements, and deriving tangent line equations. It emphasizes the interpretation of derivatives in prac...This page contains exercises on calculus derivatives, including evaluating derivatives, proving statements, and deriving tangent line equations. It emphasizes the interpretation of derivatives in practical contexts like water levels and wind speeds. The answer sections illustrate the connection between mathematical calculations and real-world applications by providing derivative functions and their evaluations at specific points.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.04%3A_Slope_FieldsThe general first order equation we are studying looks like y′=f(x,y). In general, we cannot simply solve these kinds of equations explicitly. It would be nice if we could at least figure out the sha...The general first order equation we are studying looks like y′=f(x,y). In general, we cannot simply solve these kinds of equations explicitly. It would be nice if we could at least figure out the shape and behavior of the solutions, or if we could find approximate solutions.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.04%3A_Slope_Fields/1.4E%3A_Exercises_for_Section_1.4This page contains exercises focused on differential equations and slope fields, including sketching slope fields, analyzing behaviors, and exploring the existence and uniqueness of solutions. It emph...This page contains exercises focused on differential equations and slope fields, including sketching slope fields, analyzing behaviors, and exploring the existence and uniqueness of solutions. It emphasizes continuity and differentiability in relation to Picard's theorem and tasks students with matching equations to slope fields and deducing solutions from specific values.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/01%3A_Integration/1.08%3A_Chapter_1_Review_ExercisesThis page features calculus exercises on definite integrals, Riemann sums, and antiderivatives. It includes exercises on evaluating mathematical truths and real-world applications, such as calculating...This page features calculus exercises on definite integrals, Riemann sums, and antiderivatives. It includes exercises on evaluating mathematical truths and real-world applications, such as calculating average costs and velocities. The content ranges from theoretical proofs to practical scenarios, emphasizing the continuity of functions and derivatives. Specific calculations and their answers are provided, demonstrating the connections between theory and application.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/02%3A_Multiple_Integration/2.01%3A_Double_Integrals_over_Rectangular_Regions/2.1E%3A_ExercisesThis page covers exercises on estimating volumes and integrals using numerical methods like the midpoint rule and Riemann sums for specific functions over defined regions. It includes discussions on d...This page covers exercises on estimating volumes and integrals using numerical methods like the midpoint rule and Riemann sums for specific functions over defined regions. It includes discussions on double integrals, solid geometry, and inequalities related to these integrals. The text also addresses the average value of functions, specifically calculating the average temperature across a rectangular region, with results and estimations presented in data tables.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.01%3A_Areas_between_CurvesJust as definite integrals can be used to find the area under a curve, they can also be used to find the area between two curves. To find the area between two curves defined by functions, integrate th...Just as definite integrals can be used to find the area under a curve, they can also be used to find the area between two curves. To find the area between two curves defined by functions, integrate the difference of the functions. If the graphs of the functions cross, or if the region is complex, use the absolute value of the difference of the functions. In this case, it may be necessary to evaluate two or more integrals.
- https://math.libretexts.org/Bookshelves/Analysis/Complex_Variables_with_Applications_(Orloff)/02%3A_Analytic_Functions/2.03%3A_Limits_and_Continuous_FunctionsIf h(z) is continuous and defined on a neighborhood of w1 then lim (Note: we will give the official definition of continuity in the next section.) If the fun...If h(z) is continuous and defined on a neighborhood of w_1 then \lim_{z \to z_0} h(f(z)) = h(w_1) (Note: we will give the official definition of continuity in the next section.) If the function f(z) is defined on an open disk around z_0 and \lim_{z \to z_0} f(z) = f(z_0) then we say f is continuous at z_0. If f is defined on an open region A then the phrase 'f is continuous on A' means that f is continuous at every point in A.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/02%3A_Multiple_Integration/2.03%3A_Double_Integrals_in_Polar_CoordinatesDouble integrals are sometimes much easier to evaluate if we change rectangular coordinates to polar coordinates. However, before we describe how to make this change, we need to establish the concept ...Double integrals are sometimes much easier to evaluate if we change rectangular coordinates to polar coordinates. However, before we describe how to make this change, we need to establish the concept of a double integral in a polar rectangular region.
