# Topics of the menu Analysis

- Sequences and Series (New in Version 9.0 since may 2021)
- The program determines the first n terms of a sequence (a
_{i}) and the associated series (sum of the sequence terms) if the first terms of the sequence and a recourse formula a_{i}=ƒ(a_{0}, a_{1}, ... , a_{i-1}) or an explicit function a_{i}=ƒ(i) are given. - Division of Polynomials
- The product and quotient of two polynoms will be calculated.
- Factorization of Polynomials (New in Version 9.0)
- The rational zeros and the linear factor decomposition of a polynomial are determined.
- Transformation of Polynomials (New in Version 9.0)
- A polynomial function ƒ(x) can be shifteded or stretched in the x-direction and the y-direction.
- GCD and LCM of polynomials (New in Version 9.0 since february 2021)
- The greatest common divisor (GCD) and the least common multiple (LCM) of two polynomials are determined.
- Function Plotter
- There are three plotters. One for up to ten explizit functions, one for piecewise-defined functions and one for functions in parametric representation.
- Polynomial Functions (New in Version 9.0)
- The program carries out the curve discussion for a polynomial function. This means that the derivatives and the antiderivative are determined, the function is examined for zeros, for extremes, for turning points and for symmetry.
- Rational Functions (New in Version 9.0)
- The program carries out the curve discussion for a (broken) rational function. This means that the derivations and the gaps in the domain of definition are determined. The function is examined for zeros, extremes, points of inflection and the behavior for |x|→ ∞ .
- Curve Sketching
- Examination of an arbitrary function. The derivations, zeros, extrema and points of inflection are determined.
- Newton-Iteration
- Approximation of the zeros of a function ƒ(x) by Newton's method with a first guess x
_{0}. - Series Expansion
- Plotter for functions given as a series over ƒ(x,k). You may develop the function with different parameter ranges and different y-offset.
- Integral Calculus
- The definite integral over ƒ1-ƒ2 from a to b is calculated as well as the oriented and absolut content under the curve, the twisting moments, the bodies of revolution and the centroid.
- Area Functions
- Plotter for an area function ƒ(x,y), which may contain a subterm u(x,y).

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