Intermediate value theorem

Linear Approximation Applications

Published in James K. Peterson, Basic Analysis II, 2020

The intermediate value theorem tells us that a continuous function takes on every value between two points. Hence, there is a point cx between cx+ and cx− so that uxxxx(cx,t0)=12(uxxxx(cx+,t0)+uxxxx(cx−,t0)).

Preliminaries

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Published in Ronald B. Guenther, John W. Lee, Sturm-Liouville Problems, 2018

Ronald B. Guenther, John W. Lee

(Intermediate Value Theorem) Iff(x)is a real-valued continuous function on an interval[a,b]and C is a value strictly betweenA=f(a)andB=f(b),then there is a point c with a < c < b such thatf(c)=C.

Review of PV array modelling, configuration and MPPT techniques

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Published in International Journal of Modelling and Simulation, 2022

Mohd Faisal Jalil, Shahida Khatoon, Ibraheem Nasiruddin, R. C. Bansal

The bisection method is one of the simplest techniques of finding roots of the transcendental equation. The intermediate value theorem is basis of this method that is, if a continuous function changes its polarity in a period of interval, it means that a root lies in that interval. According to this theorem, function f(x) = 0 for an interval [l, u], which accommodates a root x* of f(x). If the polarity of the function changes in an interval [l, u], then we split the interval in half, the midpoint m = (l + u)/2. The decision for orientation of change in the next halving step represented in Figure 8 is as follows:

Intermediate value theorem

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Linear Approximation Applications

Preliminaries

Review of PV array modelling, configuration and MPPT techniques