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Derivative calculators are commonly used to help solve simple differential calculus equations. Generally, they are not able to solve complex calculus equations.
Equations are not especially useful for solving most of the real-life problems that people face, which is too bad, since problems that can be reduced to equations are likely to be solved before long if not immediately. However, there are many problems in the physical sciences and engineering that lend themselves to mathematical modeling and equations and modern computer allow many difficult computations to be made quickly. Statistical methods and computer simulations can solve problems where precise equations can not be found. Also, the mental discipline developed in learning any sort of mathematics will help you develop reasoning skills that will help you solve many real life problems in the future.
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Z tranform can be used to solve the differential equations occurring in electrical problems.
There is no single method to solve all types of fraction problems. Some problems and their solutions are relatively simple, others are extremely difficult.