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Zeno of Elea
It has only been in the last century with advent of calculus that we have been able to do something never done previously. That is add up an infinite series. Centuries ago when philosophers like Zeno of Elea were around, they managed to create seeming contradictions between reality and logic. For instance, one idea went that in order to traverse any distance, you first must pass halfway, but first halfway of that, and on ad finitum. Well, that creates a problem in which movement seems only imagination as one cannot traverse an infinite number of spaces in a finite time. It turns out though that calculus is the very way that allows us to add an infinite number of values and find their sum. more info >>
This website features a web-based integral calculator that allows the computation of integrals in the user's browser. The integral calculator supports both indefinite integrals (antiderivatives) and definite integrals. If the user enters "cos(x)", the answer "sin(x)" will be given. The calculator also supports far more complex mathematical expressions including functions composed of trigonometric functions, hyperbolic functions and exponential functions (and their respective inverse functions). When computing definite integrals, improper integrals with limits such as (negative) infinity are supported as well. The integration variable can be selected by the user, and the integral calculator can optionally simplify all input and output expressions. Calculations are performed using the Computer Algebra System (CAS) "Maxima", which is one of the oldest and most robust CAS. Both the user's input and the answers are displayed as graphical formulas using MathJax. Calculations can be shared with other users. more info >>
Given a problem, CyMath shows the full solution with all steps shown. Whether it's a calculus problem involving methods of integration or differentiation, or an algebra problem involving solving for x or factoring quadratic polynomial, CyMath can help. It also contains rich reference material that is directly connected to the solver, so that the user can refer to relevant material when needed. Further, the solver formats the math expression as the user types it in. This instant feedback makes it very easy to know whether the expression is entered correctly or not. Finally, the examples page contains a library of sample problems that can be used for self testing purposes. more info >>
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