composite of a function is fog(x)=f(g(x))
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The Mandelbrot graph is generated iteratively and so is a function of a function of a function ... and in that sense it is a composite function.
Series in calculus are important for many reasons. One of them is the ability to differentiate or integrate a series that represents a function much easier than the function itself.
Differential Calculus is to take the derivative of the function. It is important as it can be applied and supports other branches of science. For ex, If you have a velocity function, you can get its acceleration function by taking its derivative, same relationship as well with area and volume formulas.
There is no Calculus function like ic 4808. Kindly check your question again.
Anti-derivatives are a part of the integrals in the calculus field. According to the site Chegg, it is best described as the "inverse operation of differentiation."