1. Consider the function 2k f(x) : k=0 defined for all x € R. (The series converges for all x E R.) f(x) – 1– 2 – x² (a) Compute lim (Note: 0° = 1.) 8x3 (b) Find f(n) (0) for all n > 0. (c) Find a power series representation for f(n) (x) for all n > 0 and all x E R.

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A: Differential Equation

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.