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Maclaurin Series
Before working any illustrations of Taylor Series the first requirement is to address the assumption that a Taylor Series will in fact exist for a specified function. Let us start out with a few notation and definitions that we'll require.
To find out a condition that must be true in order for a Taylor series to exist for a function let's first describe the nth degree Taylor polynomial of f (x) as,
.
Note: This actually is a polynomial of degree at most n! If we were to write out the sum with no the summation notation this would obviously be an nth degree polynomial.
Let 0 ! V1 ! ! Vk ! 0 be a long exact sequence of vector spaces with linear maps. Show that P (??1)i dim Vi = 0.
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assignment for appications of derivatives
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Non Linear Relationships If the correlation coefficient and the scatter diagram do not indicate linear relationship, then the relationship may be nonlinear. Two such relations
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