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• Integration
  ...heorem allows us to compute anything defined this way by means of a simple substitution -- as long as an antiderivative can be found! We will refer to them as ''in Because of the extra coefficient, the trigonometric integration formulas, such as $\int \sin x \, dx=-\cos x+C$, don't hold for
  69 KB (11,727 words) - 03:34, 30 January 2019
• Operations on functions
  i.e., the new function is given by the ''substitution formula'': \text{name of the new function}&&\quad\text{substitution}
  142 KB (23,566 words) - 02:01, 23 February 2019
• Applied Calculus -- Spring 2015
  *Chapter 5. Trigonometric Functions **5.2 The Trigonometric Functions
  9 KB (1,141 words) - 16:08, 26 April 2015
• Limits and continuity
  ...$x_n\to a$. Then we evaluate this limit of a new sequence that comes from substitution: ...e think of the sequence $x_n$ as a function, then we should interpret this substitution,
  107 KB (18,743 words) - 17:00, 10 February 2019
• Integration in dimension n
  ...[[trigonometric substitution]] for each $x$. Instead we do trigonometric" substitution for $( x, y )$ which turns into the "[[change of variables]]" and the new v where $( 9 {\Delta}W )$ equals ${\Delta}A$. Substitution and the limit and the Riemann sum of $f$, respectively, yield
  33 KB (5,415 words) - 05:58, 20 August 2011
• Calculus by Rogawski
  1.4 [[Trigonometric Functions]] 2.6 Trigonometric Limits
  6 KB (634 words) - 16:38, 1 March 2013
• Precalculus
  We then use this trigonometric identity: As we see, with the variables properly named, ''composition is substitution'', Indeed,
  100 KB (16,148 words) - 20:04, 18 January 2017
• Differential calculus of parametric curves
  ...ally, we try to ''eliminate the parameter'' by solving for $t$ followed by substitution: Thus, the limits of continuous functions can be found by ''substitution''.
  130 KB (22,842 words) - 13:52, 24 November 2018
• Differentiation
  Therefore, the trigonometric differentiation formulas, such as $\left( \sin x \right)'=\cos x$, don't ho \small\text{substitution }&\quad \da{u=g(x)} & &\ \ \ua{CR} \\
  82 KB (14,116 words) - 19:50, 6 December 2018
• The derivative
  Thus, what this substitution accomplished is a ''change of variables'' in the limit. &\to 2 + 0&\to 2a + 0&\to 2x + 0&\text{The limit is evaluated by substitution...}\\
  75 KB (13,000 words) - 15:12, 7 December 2018
• Sphere
  ...[[trigonometric substitution]] for each $x$. Instead we do trigonometric" substitution for $( x, y )$ which turns into the "[[change of variables]]" and the new v
  2 KB (295 words) - 22:29, 3 September 2011
• Calculus by Stewart
  ...ter. The [[product rule|product]] and [[quotient rule]]s. Derivatives of [[trigonometric functions]]. The [[chain rule]]. Applied project: where should a pilot star ..., Leibniz, and the invention of calculus. The [[integration by subtitution|substitution]] rule.
  6 KB (794 words) - 16:29, 13 August 2017
• Differential calculus
  ...nts can be arbitrary; it is $0$ for $f(x)=x^3$ at $0$ and non-zero for the trigonometric functions below. ...ng equations, we can easily confirm that our computations were correct, by substitution. In this case, we ''differentiate the antiderivative'':
  84 KB (14,321 words) - 00:49, 7 December 2018
• Calculus II -- Fall 2014
  7.2 Trigonometric Integrals 7.3 Trigonometric Substitution
  5 KB (744 words) - 02:44, 10 December 2014
• Calculus I -- Fall 2016
  ...functions, rational functions, exponential and logarithmic functions, and trigonometric functions. ...erval. Slope of a tangent line. Derivatives of polynomials. Derivatives of trigonometric functions. Derivatives of exponential and logarithmic functions. Rules for
  11 KB (1,671 words) - 23:11, 13 December 2016
• Calculus I -- Fall 2017
  ...functions, rational functions, exponential and logarithmic functions, and trigonometric functions. ...erval. Slope of a tangent line. Derivatives of polynomials. Derivatives of trigonometric functions. Derivatives of exponential and logarithmic functions. Rules for
  13 KB (2,075 words) - 13:35, 27 November 2017
• Calculus I -- Fall 2018
  ...functions, rational functions, exponential and logarithmic functions, and trigonometric functions. ...erval. Slope of a tangent line. Derivatives of polynomials. Derivatives of trigonometric functions. Derivatives of exponential and logarithmic functions. Rules for
  8 KB (1,184 words) - 17:55, 29 October 2018
• Calculus I -- Spring 2017
  ...functions, rational functions, exponential and logarithmic functions, and trigonometric functions. ...erval. Slope of a tangent line. Derivatives of polynomials. Derivatives of trigonometric functions. Derivatives of exponential and logarithmic functions. Rules for
  12 KB (1,803 words) - 20:50, 1 May 2017
• Calculus Illustrated
  13 Trigonometric functions 2 Integration by substitution: compositions
  16 KB (1,933 words) - 19:50, 28 June 2021
• Partial differential equations
  The result of the substitution is the following equation: The ''new unknown function'' is the result of the substitution:
  53 KB (9,682 words) - 23:19, 18 November 2018

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