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• Calculus 1: exercises
  *Sketch the graph of a function f that has the following property: f is increasing and concave down on $[-1,1]$. *$f′(x)=(e^{x})².$ (a) On what intervals, if any, if f increasing? (b) On which intervals, if any, is f concave down? (c) Sketch the grap
  3 KB (435 words) - 19:23, 13 June 2011
• Parametric complexes
  ...mplex, one considers all thresholds and all possible cell complexes. Since increasing threshold $r$ enlarges the corresponding complex, we have a sequence of com ...subsections: (a) the Vietoris-Rips construction of the circle, and (b) the increasing resolution of the triangle.
  45 KB (7,255 words) - 03:59, 29 November 2015
• Preview of calculus: part 3
  Indeed term "exponential growth" makes sense: \( a ^{x} \) is ''[[increasing]]'' for \( a > 1 \). a^{x} & \textrm{ is increasing if } a > 1 \\
  17 KB (2,498 words) - 15:06, 19 March 2011
• Functions of several variables
  ...variable. This is how the concavity with respect to $x$ is increasing with increasing $y$:
  97 KB (17,654 words) - 13:59, 24 November 2018
• Geometry
  ...it is sufficient to know the sign of the derivative to distinguish between increasing and decreasing behavior. Therefore, this behavior depends only on the topol ...g, the sign of the exterior derivative will tell us the difference between increasing and decreasing behavior. But the derivative only uses the topological prope
  41 KB (6,928 words) - 17:31, 26 October 2015
• Convergence of the discrete to the continuous
  But does the latter approximate the former? Will increasing the “resolution” of the discretization allow us to recover the original ...his problem the same way one would deal with other accuracy problems -- by increasing the resolution of the image. In fact, a curve can be approximated by a digi
  21 KB (3,664 words) - 02:02, 18 July 2018
• Differential calculus of parametric curves
  ...n the curve is oriented, i.e., its direction is indicated, and $t=g(s)$ is increasing. Now assuming that $s$ is increasing with respect to $t$ (same direction!), we have a convenient way to describe
  130 KB (22,842 words) - 13:52, 24 November 2018
• Applied Calculus -- Spring 2015
  **3.1 Increasing and Decreasing Functions **3.1 Increasing and Decreasing Functions
  9 KB (1,141 words) - 16:08, 26 April 2015
• Calculus 1: midterm 2
  ...ncreasing at a rate of 5 cm²/sec. At what rate is the radius of the circle increasing when the area is 2 cm?
  991 bytes (164 words) - 20:21, 13 June 2011
• Precalculus exercises
  *Prove, from the definition, that the function $f(x)=x^2+1$ is increasing for $x>0$. ...n below. Describe its behavior the function using words “decreasing” and “increasing”.
  17 KB (2,933 words) - 19:37, 30 July 2018
• Calculus 1: midterm 2 solutions
  ...t a rate of 5 cm²/sec. At what rate is the radius of the circle increasing when the area is 2cm?
  3 KB (458 words) - 04:13, 21 May 2011
• Preview of calculus
  ...reas by filling them with increasing number of rectangles or triangles and increasing the number of sides with each step. We can then calculate the area by calcu
  4 KB (703 words) - 14:34, 9 September 2016
• Calculus 1: test 2
  ...reasing at a rate of $5$ cm²/sec. At what rate is the radius of the circle increasing when the area is $2$ cm?
  976 bytes (164 words) - 20:22, 13 June 2011
• Series
  '''Proof.''' First, the sequence of partial sums of this series is ''increasing'': ...partial sums of a series $\sum a_n$ with non-negative terms, $a_n>0$, is ''increasing'':
  113 KB (19,100 words) - 23:07, 3 January 2019
• Calculus II -- Fall 2018 -- midterm
  ...creasing or decreasing; (b) $b_n\to +\infty$ as $n\to \infty$ but it's not increasing.
  1 KB (246 words) - 19:10, 31 October 2018
• Social choice
  ...usly increases or decreases in both locations. Such a function can only be increasing or decreasing, i.e., monotonic. ...es are computed and displayed on the right. The scores for $A, ..., J$ are increasing in the obvious way: from $0$ to $.1$. In particular, $F$ is $\#$5.
  47 KB (8,030 words) - 18:48, 30 November 2015
• Calculus of chain maps
  '''Theorem (Monotonicity).''' A $0$-chain map is increasing (decreasing) on an interval if and only if its exterior derivative is posit '''Theorem (Monotonicity).''' A $0$-chain map is increasing (decreasing) on an interval if and only if its derivative is positive (nega
  41 KB (7,344 words) - 12:52, 25 July 2016
• Metric tensor
  ...it is sufficient to know the sign of the derivative to distinguish between increasing and decreasing behavior. Therefore, this behavior depends only on the topol ...g, the sign of the exterior derivative will tell us the difference between increasing and decreasing behavior. But the derivative only uses the topological prope
  42 KB (7,131 words) - 17:31, 30 November 2015
• Connectivity
  ...nly by choosing more and more complex ways to compute the length (roughly, increasing the degree of the approximation of the curve). The choice of connectivity i
  4 KB (636 words) - 14:53, 9 October 2010
• Robustness of topology of digital images and point clouds by Saveliev
  Since increasing threshold $r$ enlarges the
  27 KB (4,547 words) - 04:08, 6 November 2012

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