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- 2.1 [[Limit]]s, Rates of Change, and [[Tangent Line]]s ==Chapter 16: Line and Surface Integrals==6 KB (634 words) - 16:38, 1 March 2013
- ...'differentiation''. Given a function defined at several points of the real line, the difference quotient at that point is a way of encoding the small-scale ...hat is, if the [[Graph of a function|graph]] of the function is a straight line), then the function can be written as $y=mx + b$, where $x$ is the independ27 KB (4,329 words) - 16:02, 1 September 2019
- [[Image:tangent line examples.jpg|center]] ...[[tangent line]] to the circle at any point: the [[slope]] of the tangent line is equal to the value of the [[derivative]] of $f$ at the point.34 KB (5,665 words) - 15:12, 13 November 2012
- Then each equivalence class is a line: ...appear to be in a 1-1 correspondence with the points of the other diagonal line $y=-x$.28 KB (4,685 words) - 17:25, 28 November 2015
- ...he simplest setting, we deal with the intervals in the complex of the real line ${\mathbb R}$. Then the cochain assigns a number to each interval to indica One should recognize the second line as a line integral:25 KB (4,238 words) - 02:30, 6 April 2016
- 8. Evaluate the line integral $\int_{C}x^{2}y^{3}dx-y\sqrt{x}dy$, where $C$ is parametrized by 9. (a) Explain what it means for a line integral $\int_{C}\mathbf{F}\cdot d\mathbf{r}$ to be independent of path. (4 KB (652 words) - 15:22, 9 March 2014
- ...line segment (the path that lies on the hill) will be labeled as A and the line that lies on flat ground will be labeled as B. As for the x variable that **Number systems. Distance formula. Slope of a line. Standard equations of lines.13 KB (2,075 words) - 13:35, 27 November 2017
- ...e above formula still applies but, as we add them together, we produce a ''line integral'': ...varphi =fdx+gdy$ we construct a $0$-form $\psi$ with $d\psi =\varphi$ as a line integral. We fix a point $a \in {\bf R}^n$ and define $\psi$ as a function4 KB (778 words) - 16:47, 16 July 2014
- Then each equivalence class is a line: ...which appear in a 1-1 correspondence with the points on the other diagonal line.6 KB (1,115 words) - 16:03, 27 August 2015
- [[Image:tangent line examples.jpg|center]] ...[[tangent line]] to the circle at any point: the [[slope]] of the tangent line is equal to the value of the [[derivative]] of $f$ at the point.4 KB (662 words) - 15:17, 13 November 2012
- '''Answer:''' It's a line. Prove ${\rm span \hspace{3pt}} S = L$, the line diagonal through $0$.10 KB (1,614 words) - 17:13, 22 May 2012
- We know that the [[tangent line]] "approximates" the [[graphs of functions|graph]] of $y=f(x)$ around $x=a$ ...case, when you zoom in on the point, the tangent line will (but any other line won't) merge with the graph. This is the geometric meaning of ''best approx2 KB (384 words) - 15:44, 2 May 2011
- **0.1 The Real Number Line and Order **0.2 Absolute Value and Distance on the Real Number Line9 KB (1,141 words) - 16:08, 26 April 2015
- ...ment 1: with light from a star passing the sun and deviating from straight line. by using the graph of $f$. But for $dy$, we use the tangent line instead:10 KB (1,588 words) - 17:11, 27 August 2015
- Here $f^{-1}(A)$ is all these points, a whole line! Why? Because: there is no change of $F$ in this direction. ...tersection of these planes is "[[transversal]]", so that it's a line. This line approximates the intersection of the graph with the plane. It turns out to9 KB (1,542 words) - 19:58, 21 January 2014
- The bottom line: the numerical/computational aspect should be built in! ...s. [[Vectors]]. The [[dot product]]. The [[cross product]]. Equations of [[line|lines]] and [[plane]]s. [[Vector functions]] and space curves. Derivatives8 KB (1,196 words) - 13:02, 24 August 2015
- ...the graph of a function of two variables and the flow seems to follow the line fastest descent; maybe our vector field is the gradient of this function? W ...h ''linear functions''. In other words, what if we travel along a straight line on a flat, not necessarily horizontal, surface (maybe a roof)? After this s74 KB (13,039 words) - 14:05, 24 November 2018
- ...all vectors perpendicular to $x$? Let's call this set $S$. What is $S$? A line: ...ll vectors perpendicular to hyperplane $S$, then $Q = {\rm span}\{v \}$, a line through $0$, a $1$-dimensional subspace.</center>21 KB (3,396 words) - 20:31, 10 August 2011
- \text{the line touching the curve at a point }&\text{ the area enclosed by the curve }\ \ ...continuous. We know that the area of a trapezoid is the length of the mid-line times the height. Then we have:66 KB (11,473 words) - 21:36, 19 January 2019
- ...varphi =fdx+gdy$ we construct a $0$-form $\psi$ with $d\psi =\varphi$ as a line integral. We fix a point $a \in {\bf R}^n$ and define $\psi$ as a function [[image:line integral for PL.png|center]]8 KB (1,421 words) - 13:41, 10 April 2013