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Topic: Intermediate value theorem

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	Intermediate value theorem - Wikipedia, the free encyclopedia
		The intermediate value theorem states the following: Suppose that I is an interval in the real numbers R and that f : I → R is a continuous function.
		Darboux's theorem states that all functions that result from the differentiation of some other function on some interval have the intermediate value property (even though they need not be continuous).
		The intermediate value theorem of integration is derived from the mean value theorem and states:
	www.wikipedia.org /wiki/Intermediate_value_theorem (797 words)

	Encyclopedia: Intermediate value theorem
		The intermediate value theorem can be seen as a consequence of the following two statements from topology: Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces.
		Darbouxs theorem is a theorem in symplectic topology which states that every symplectic manifold (of fixed dimension) is locally symplectomorphic.
		The intermediate value theorem of integration is derived from the mean value theorem and states: Integration may be any of the following: In the most general sense, integration may be any bringing together of things: the integration of two or more economies, cultures, religions (usually called syncretism), etc....
	www.nationmaster.com /encyclopedia/Intermediate-value-theorem (1346 words)

	Intermediate value theorem: Definition and Links by Encyclopedian.com - All about Intermediate value theorem (Site not responding. Last check: 2007-11-07)
		The Intermediate value theorem in calculus states the following: Suppose that I is an interval in the real numbers R and that f : I
		The intermediate value theorem is in essence equivalent to Rolle's theorem.
		In integration the intermediate value theorem has a different twist.
	www.encyclopedian.com /in/Intermediate-value-theorem.html (507 words)

	Properties of Continuous Functions
		As an application of the Intermediate Value Theorem, we discuss the existence of roots of continuous functions and the bisection method for finding roots.
		One of the useful consequences of the Intermediate Value Theorem is the following.
		While the Extreme Value Theorem may seem intuitively obvious, it is a difficult theorem to prove.
	archives.math.utk.edu /visual.calculus/1/continuous.7 (356 words)

	The Intermediate Value Theorem states (Site not responding. Last check: 2007-11-07)
		A frequent use of this theorem is in proving the existence of roots of function.
		For the first function, f(x) has only two values, 0 or 1.While it is defined for all x in the closed interval, it is not continuous but is a step function.
		For the second function, is not defined for all values of x in the interval, rather, it has a hole at x = ½.
	members.uia.net /tajames/calculus/notes-IVT.html (215 words)

	Rolle and the Mean Value Theorem
		Theorem 5.15 (Rolle's Theorem) Let f be continuous on [a, b], and differentiable on (a, b), and suppose that
		Theorem 5.18 (The Mean Value Theorem) Let f be continuous on [a, b], and differentiable on (a, b).
		Theorem 5.21 (The Cauchy Mean Value Theorem) Let f and g be both continuous on [a, b] and differentiable on (a, b).
	www.maths.abdn.ac.uk /~igc/tch/ma2001/notes/node42.html (862 words)

	Mean-value Theorem (Site not responding. Last check: 2007-11-07)
		Mean value theorem for continuous vector functions by smooth approximations...
		The Mean Value Theorem for integrals of continuous functions...
		EconPapers: Mean value theorem for continuous vector functions by smooth approxi...
	www.scienceoxygen.com /math/174.html (179 words)

	UCES Methods and Analysis Chap. 2.1: Nonlinear Probs and Intermediate Values
		In the next section the mean value theorem will be proved using the assumption of a continuous derivative and the intermediate value theorem.
		The first will be the intermediate value theorem which will helps us establish the convergence of the bisection algorithm.
		The mean value theorem is a fundamental tool for the analysis of the rates of convergence of algorithms.
	www.krellinst.org /UCES/archive/classes/CNA/dir2.1/uces2.1.html (977 words)

	intermediate value theorem (Site not responding. Last check: 2007-11-07)
		AMCA: The Intermediate Value Theorem for $f$-Rings by Suzanne Larson...
		Sarkovskii's theorem and the islands of stability in the cascade diagram...
		Intermediate Value Theorem and Thickness of Simple Closed Curves...
	www.scienceoxygen.com /math/368.html (214 words)

	Fixed-Point Theorems
		Fixed-point theorems are one of the major tools economists use for proving existence, etc.
		One of the oldest fixed-point theorems - Brouwer's - was developed in 1910 and already by 1928, John von Neumann was using it to prove the existence of a "minimax" solution to two-agent games (which translates itself mathematically into the existence of a saddlepoint).
		Brouwer's Theorem made a reapparence in Lionel McKenzie (1959), Hirofumi Uzawa (1962) and, later, in the computational work of Herbert Scarf (1973).
	cepa.newschool.edu /het/essays/math/fixedpoint.htm (544 words)

	Chickscope: Explore: EggMath: The White/Yolk Theorem
		This is a two-dimensional analog of the intermediate-value theorem; it is the two-dimensional case of the Borsuk-Ulam theorem.
		The Borsuk-Ulam theorem in general dimensions can be stated in a number of ways but always deals with a map d from sphere to sphere or from sphere to euclidean space which is odd, meaning that d(-s)=-d(s).
		The usual proof of the theorem is by induction.
	chickscope.beckman.uiuc.edu /explore/eggmath/wy/borsuk.html (967 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Thus, by the IVT, the root is between \+ 1.2207440 and 1.2207445.
		Thus, by the IVT, the root \+ is between 1.22074405 and 1.2207441.
		Thus, by the IVT, the solution (root) is between 1.22074408 and 1.2 2074409.
	www.math.utoledo.edu /~anderson/1780/MapleActivities/Act4IVT.mws (649 words)

	Derivative Theorems Part I
		Rolle's theorem says that if a ball is thrown up and comes back down, then at some time along its journey it is neither going up or down, i.e., it reaches a maximum.
		The mean value theorem states that the instantaneous velocity equals the average velocity somewhere along the trip.
		The extreme value theorem tell us that all continuous function reach a top and a bottom.
	www.ltcconline.net /greenl/courses/105/theoremsrelatedrates/DERTHEOR.HTM (148 words)

	Intermediate Value Theorem (Site not responding. Last check: 2007-11-07)
		If v is positive then values of x near u have f(x) positive, and u is not the least upper bound.
		This theorem remains valid if the domain is n dimensional space, or even generalized euclidean space.
		If the bottom of the hill is at sea level, and the top of the hill is 1,000 meters high, there is some point on the hill with elevation 374 meters.
	www.mathreference.com /top-ms,ivt.html (241 words)

	Calculus:Applications of Derivatives - Wikibooks
		A minimum or maximum is the function value at which a function has the lowest or highest value or values.
		Since f is continuous except for at 0, we can use the Intermediate Value Theorem find out whether they are minima, maxima, or nothing at all by picking intermediate values and checking them.
		We now pick intermediate values and test to see whether they show that the function value indicates an extreme value.
	en.wikibooks.org /wiki/Calculus:Applications (413 words)

	mbox: Re: Intermediate Value Theorem (Site not responding. Last check: 2007-11-07)
		That's why the intermediate value theorem can be proved in constructive mathematics inside the world of real numbers.
		The point I wanted to make is: The intermediate value theorem for polynomials (to be precise: of a given degree) is a statement that uses real numbers as primitive unstructured objects and involves only addition and multiplication.
		This suggestion can be easily extracted from the theorem if the theorem is stated in a well-typed language and in many cases such a suggestion will be helpful, notably if automated provers are used.
	www-unix.mcs.anl.gov /qed/mail-archive/volume-2/0010.html (337 words)

	Intermediate value theorem (Site not responding. Last check: 2007-11-07)
		[[Image Link]] The intermediate value theorem of calculus states the following: Suppose that I is an interval in the real numbers R and that f : I
		For u=0 above, it is also known as Bolzano's theorem and follows immediately from the intermediate value theorem of calculus.
		This theorem was first stated, together with a proof which used techniques which are now regarded as non-rigorous, by Bernard Bolzano.
	www.sciencedaily.com /encyclopedia/intermediate_value_theorem (477 words)

	The intermediate value theorem (Site not responding. Last check: 2007-11-07)
		The intermediate value theorem can be used to prove a variety of simple "real-life" results.
		Hence (by the intermediate value theorem) there is an intermediate position where exactly half is at one side.
		Now less than half the beans are on the left and so you passed through an intermediate position where both beans and potatoes were divided fairly.
	www-groups.dcs.st-and.ac.uk /~john/analysis/Lectures/L20.html (691 words)

	Lecture 16: Functions (Site not responding. Last check: 2007-11-07)
		The Intermediate Value Theorem states that every function which is continuous over an interval of numbers has the intermediate value property over that interval.
		The intermediate value property over the interval [a,b] states the following: if the number M is caught between f(a) and f(b), then there is a number c in the interval [a,b] such that f(c)=M. This useful theorem is important in isolating the roots of a polynomial and of other continuous functions.
		If we find that for polynomial p, p(a) is negative and p(b) is positive, then the theorem states that p has a root between a and b.
	www.math.uncc.edu /~hbreiter/m1120/lectures/lect16.htm (172 words)

	Intermediate Value Theorem Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-11-07)
		Looking For intermediate value theorem - Find intermediate value theorem and more at Lycos Search.
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	www.karr.net /search/encyclopedia/Intermediate_value_theorem (906 words)

	Mean Value Theorem for Integrals (Site not responding. Last check: 2007-11-07)
		A mean value theorem for zeta functions associated with positive definite integr...
		Using the mean value theorem for integrals to finish the proof of FTC...
		IngentaConnect A converse of the mean value theorem for integrals...
	www.scienceoxygen.com /math/184.html (120 words)

	Intermediate value theorem (Site not responding. Last check: 2007-11-07)
		Intermediate Value Theorem of CalculusThe Intermediate value theorem in calculus states the following: Suppose that I is an interval in the real numbers R and that f : I -> R is a continuous function.
		All is still licensed under the GNU FDL.
		Vexed in the squally seas as we lay by Capraja and Elba, Looking around on the waste of the rushing incurious.
	www.termsdefined.net /in/intermediate-value-theorem.html (708 words)

	Intermediate Value Theorem (Site not responding. Last check: 2007-11-07)
		Then the Intermediate Value Theorem says that for any value k where k is between f(a) and f(b), there exists a value c
		This theorem is often used to show that a function has a zero between two given x values, but that is just a special case of the theorem.
		Thus by the Intermediate Value Theorem g(x) must equal 5000 for some x between 10 and 15.
	www.lansing.cc.mi.us /~lshears/math121/lecture_notes/unit5/intm_vl_thm (287 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Extreme Value Theorem (note that it only applies to continuous functions on closed intervals; guarantees the existence of an absolute maximum and minimum value of f)
		A function can have at most one absolute maximum value on an interval, but it may attain that maximum at many different points.
		Using the IVT to guarantee the existence of a root of a function
	www.rhodes.edu /mathcs/faculty/shelton/Classes/Fall03/Math121/m121sep19.html (125 words)

	Bolzano
		Nevertheless this property does not hold for all values of i without restriction, namely not for an i = b - a, for fb is already > gb.
		And consequently it would not be true that u is the greatest of the values for which the assertion holds, that all lower values of i make f(a + i) < g(a + i); for u + w would be a still greater value for which this holds.
		The theorem is proved by showing that those values of i of which it can be asserted that all smaller values possess property M and those of which this cannot be asserted can be brought as near one another as desired.
	www.maths.uwa.edu.au /~schultz/3M3/L26Bolzano.html (1642 words)

	2. (Site not responding. Last check: 2007-11-07)
		The value of the definite integral of a function f(x) depends on the choice of the two limits of integration a and b; it is a function of the lower limit a as well as of the upper limit b.
		Prove, using the mean value theorem of the integral calculus, that the derivative of the indefinite integral of f(x) is equal to f(x).
		Finally, it should be observed that in the present discussion of the mean value theorem of the differential calculus we have had to make assumptions more stringent than the theorems themselves require.
	kr.cs.ait.ac.th /~radok/math/mat6/calc22.htm (5879 words)

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