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gradient | the gradient of the function f(x,y) is defined to be \vecs ∇f(x,y)=(∂f/∂x)\,\hat{\mathbf i}+(∂f/∂y)\,\hat{\mathbf j}, which can be generalized to a function of any number of independent variables gradient field | a vector field \vecs{F} for which there exists a scalar function f such that \vecs ∇f=\vecs{F}; ...
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instantaneous velocity | The instantaneous velocity of an object with a position function that is given by s(t) is the value that the average velocities on intervals of the form [t,a] and [a,t] approach as the values of t move closer to a, provided such a value exists integrable function | a function is integrable if t...
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linearly dependent | a set of functions f_1(x),f_2(x),…,f_n(x) for whichthere are constants c_1,c_2,…c_n, not all zero, such that c_1f_1(x)+c_2f_2(x)+⋯ +c_nf_n(x)=0 for all \(x\) in the interval of interest linearly independent | a set of functions f_1(x),f_2(x),…,f_n(x) for which there are no constants c_1,c_2,…c_n, s...
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normal component of acceleration | the coefficient of the unit normal vector \vecs N when the acceleration vector is written as a linear combination of \vecs T and \vecs N normal plane | a plane that is perpendicular to a curve at any point on the curve normal vector | a vector perpendicular to a plane normalization | ...
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polar axis | the horizontal axis in the polar coordinate system corresponding to r≥0 polar coordinate system | a system for locating points in the plane. The coordinates are r, the radial coordinate, and θ, the angular coordinate polar equation | an equation or function relating the radial coordinate to the angular coo...
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right-endpoint approximation | the right-endpoint approximation is an approximation of the area of the rectangles under a curve using the right endpoint of each subinterval to construct the vertical sides of each rectangle right-hand rule | a common way to define the orientation of the three-dimensional coordinate syst...
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standard equation of a sphere | (x−a)^2+(y−b)^2+(z−c)^2=r^2 describes a sphere with center (a,b,c) and radius r standard form | the form of a first-order linear differential equation obtained by writing the differential equation in the form y'+p(x)y=q(x) standard form | an equation of a conic section showing its proper...
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trace | the intersection of a three-dimensional surface with a coordinate plane transcendental function | a function that cannot be expressed by a combination of basic arithmetic operations transformation | a function that transforms a region GG in one plane into a region RR in another plane by a change of variables tr...
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work done by a force | work is generally thought of as the amount of energy it takes to move an object; if we represent an applied force by a vector \vecs{ F} and the displacement of an object by a vector \vecs{ s}, then the work done by the force is the dot product of \vecs{ F} and \vecs{ s}. zero vector | the vector ...
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Detailed Licensing Overview Title: Calculus (OpenStax) Webpages: 285 Applicable Restrictions: Noncommercial All licenses found: CC BY-NC-SA 4.0: 99.6% (284 pages) Undeclared: 0.4% (1 page) By Page Calculus (OpenStax) - CC BY-NC-SA 4.0 2.3E: Exercises for Section 2.3 - CC BY-NC-SA Front Matter - CC BY-NC-SA 4.0 4.0 Titl...
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3.7E: Exercises for Section 3.7 - CC BY-NC-SA 4.R: Chapter 4 Review Exercises - CC BY-NC-SA 4.0 4.0 5: Integration - CC BY-NC-SA 4.0 3.8: Implicit Differentiation - CC BY-NC-SA 4.0 5.0: Prelude to Integration - CC BY-NC-SA 4.0 3.8E: Exercises for Section 3.8 - CC BY-NC-SA 5.1: Approximating Areas - CC BY-NC-SA 4.0 4.0 ...
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6.4E: Exercises for Section 6.4 - CC BY-NC-SA 7.7E: Exercises for Section 7.7 - CC BY-NC-SA 4.0 4.0 6.5: Physical Applications of Integration - CC BY- 7.R: Chapter 7 Review Exercises - CC BY-NC-SA 4.0 NC-SA 4.0 8: Introduction to Differential Equations - CC BY-NC-SA 6.5E: Exercises for Section 6.5 - CC BY-NC-SA 4.0 4.0...
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9.R: Chapter 9 Review Exercises - CC BY-NC-SA 4.0 12.2: Vectors in Three Dimensions - CC BY-NC-SA 10: Power Series - CC BY-NC-SA 4.0 4.0 10.0: Prelude to Power Series - CC BY-NC-SA 4.0 12.2E: Exercises for Section 12.2 - CC BY-NC-SA 10.1: Power Series and Functions - CC BY-NC-SA 4.0 4.0 10.1E: Exercises for Section 10....
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14.1E: Exercises for Section 14.1 - CC BY-NC-SA 15.5E: Exercises for Section 15.5 - CC BY-NC-SA 4.0 4.0 14.2: Limits and Continuity - CC BY-NC-SA 4.0 15.6: Calculating Centers of Mass and Moments of 14.2E: Exercises for Section 14.2 - CC BY-NC-SA Inertia - CC BY-NC-SA 4.0 4.0 15.6E: Exercises for Section 15.6 - CC BY-N...
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17.1E: Exercises for Section 17.1 - CC BY-NC-SA 17.4E: Exercises for Section 17.4 - CC BY-NC-SA 4.0 4.0 17.2: Nonhomogeneous Linear Equations - CC BY- 17.R: Chapter 17 Review Exercises - CC BY-NC-SA NC-SA 4.0 4.0 17.2E: Exercises for Section 17.2 - CC BY-NC-SA Appendices - CC BY-NC-SA 4.0 4.0 Appendix A: Table of Deriv...
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