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• Vector calculus: exercises
  Find a tangent line to the curve parameterized by $f$ at the point $t=2$. ...Therefore, it suffices to simply use $f'(2)$ as a direction vector for the line. Further
  16 KB (2,457 words) - 02:17, 22 August 2011
• Continuous functions
  '''Exercise.''' To what is the Mobius band with the center line cut out homeomorphic? [[Image:point-point line.png|center]]
  42 KB (7,138 words) - 19:08, 28 November 2015
• Vector calculus: review
  #In an effort to find the line in which the planes $ 2x -y- z=2 $ and $-4x+2y+2z=1$ intersect, a student #Parametrically describe the line segment with endpoints $(-1,-1,-1)$ and $(1,1,1).$
  7 KB (1,394 words) - 02:36, 22 August 2011
• Derivative
  [[Image:tangent line examples.jpg|right]] ...circle]]. Then we [[differentiation|differentiate]] and find the [[tangent line]] to the circle at any point:
  4 KB (659 words) - 01:47, 30 August 2010
• What shape of sword is best for cutting?
  [[image:rotated straight line.png| center]] The first example is a ''straight line'' (curvature $0$):
  14 KB (2,504 words) - 14:59, 17 September 2019
• Differentials
  ...\frac{dy}{dx}\bigg| _a$ = the derivative at $a$ = the slope of the tangent line through $(a,f(a))$ = $\frac{rise}{run}$ </center> The slope of the [[secant line]] is $m = \frac{\Delta y}{\Delta x}$, or
  1 KB (243 words) - 18:13, 22 August 2015
• Integral theorems of vector calculus
  ...now. Then, in a similar way, an [[area integral]] can be expressed as a [[line integral]], somehow: ...} FTC) \hspace{3pt} (interpret \hspace{3pt} as \hspace{3pt} a \hspace{3pt} line \hspace{3pt} integral)} \\
  16 KB (2,752 words) - 14:18, 28 December 2012
• Affine approximation
  As the picture shows, a curve is approximated by a straight line while a [[surface]] by a plane. ...in on the graph of a [[differentiable function]], it looks like a straight line.
  7 KB (1,162 words) - 03:25, 22 August 2011
• Limits: part 1
  **on the line through $A$ that is perpendicular to the diagonal, Estimate the [[tangent line]] of a function given [[numerical representation of functions|numerically]]
  10 KB (1,609 words) - 16:13, 2 May 2011
• Applications of derivative: optimization
  Find a point on the line $y=4x + 7$ closest to the origin. [[Image:Origin.png|none|Closest distance to origin for line $y = 4x + 7$.]]
  6 KB (891 words) - 02:15, 17 July 2011
• Metric complexes
  The arc-length is an example of a ''line integral''<!--\index{line integral}--> of a $1$-form $\rho$ over a $1$-chain $a$ in complex $K$ equip What's left? The complex $K$ must be a complex representation of the infinite line or the circle:
  35 KB (5,871 words) - 22:43, 7 April 2016
• Metric tensor
  The arc-length is an example of a ''line integral''<!--\index{line integral}--> of a $1$-form $\rho$ over a $1$-chain $a$ in complex $K$ equip What's left? The complex $K$ has to be a complex representation of the line or the circle:
  42 KB (7,131 words) - 17:31, 30 November 2015
• Polar coordinates
  1) line r = 0: F( 0, θ ) = ( 0, 0 );
  1 KB (167 words) - 02:30, 18 August 2010
• Homeomorphism
  [[Image:point-point line.png|center]] ...(a,c)$ and $(b,d)$, so its slope is $m = \frac{d-c}{b-a}\ne 0$. Hence, the line is given by
  13 KB (2,168 words) - 13:09, 7 August 2014
• Preview of calculus: part 3
  ...'s the [[natural base]] exponent. It has a special property: the [[tangent line]] at the y-intercept has 45 degree [[slope]], below: ...tal Line Test.''' A function is one-to-one if and only if every horizontal line has at most one intersection with its graph.
  17 KB (2,498 words) - 15:06, 19 March 2011
• Implicit differentiation
  ...to f^{\prime} \to $ tangent. This is not a graph because of the [[vertical line test]]. What do we do? To find it, I need the [[derivative]], but there is '''Example, Circle.''' Find the [[tangent line]] for the [[circle]] with radius 1 at the point $(\frac{\sqrt{2}}{2},\frac{
  9 KB (1,445 words) - 15:50, 2 May 2011
• Quality of soldering
  The area inside the red contour (i.e., inside your red line) is 140,582 pixels. So the proportion of gray inside the red line is
  3 KB (532 words) - 16:22, 4 March 2011
• Derivative as a function
  *Differentiable : There is a tangent line. [[Image:Cusp.png|Which line is the tangent?]]
  9 KB (1,437 words) - 14:05, 7 October 2012
• Quotients
  ...$x$-axis. Hence, the quotient set corresponds, in this sense, to the real line. Algebraically, we write: ...te a circle<!--\index{circle}-->. An insightful way is to make it from the line. One just winds the helix, which is ${\bf R}$ topologically, around the cir
  26 KB (4,538 words) - 23:15, 26 November 2015
• Discrete forms and cochains
  ...$f$ -- a discrete function $g$ defined at predetermined points of the real line. What is its derivative? ...aluated at one of the intervals rather than a point -- is the slope of the line that connects the end-points of the interval.
  34 KB (5,619 words) - 16:00, 30 November 2015

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