Why does the Weierstrass substitution work?
Any rational expression of trigonometric functions can be always reduced to integrating a rational function by making the Weierstrass substitution. The Weierstrass substitution is very useful for integrals involving a simple rational expression in and/or in the denominator.
What is the T formula?
Introducing the parameter t=tanθ2 turns out to be a very useful tool in solving certain types of trigonometric equations and also in finding certain integrals involving trigonometric functions. The basic idea is to relate sinθ, cosθ and even tanθ to the tangent of half the angle.
Why do we use trigonometric substitution?
In mathematics, trigonometric substitution is the substitution of trigonometric functions for other expressions. In calculus, trigonometric substitution is a technique for evaluating integrals. Moreover, one may use the trigonometric identities to simplify certain integrals containing radical expressions.
How do you use the Weierstrass approximation theorem?
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as desired by a polynomial function….External links.
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Other | Microsoft Academic SUDOC (France) 1 |
Why is the Bolzano Weierstrass theorem important?
A very important theorem about subsequences was introduced by Bernhard Bolzano and, later, independently proven by Karl Weierstrass. Basically, this theorem says that any bounded sequence of real numbers has a convergent subsequence.
Which of the following function is nowhere differentiable?
). These functions are simply termed continuous nowhere differentiable functions. with a odd, 01+32π b > 1 + 3 2 ….References.
Title | nowhere differentiable |
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Defines | nowhere differentiable curve |
How do you find t Stat?
Calculate the T-statistic Subtract the population mean from the sample mean: x-bar – μ. Divide s by the square root of n, the number of units in the sample: s ÷ √(n).