Problem Statement: Let f(x) = In this problem we create power series representations for f 2 – 2 centered at c, where c is a real number. (a) Find a power series representation of f(x) centered at c = 0. What is the interval of convergence for this power series representation? (b) Find a power series representation of f(x) centered at c = 1. What is the interval of convergence for this power series representation? (c) Find a power series representation of f(x) centered at c = -1. What is the interval of convergence for this power series representation? (d) Find a power series representation of f(x) centered at e = 10. What is the interval of convergence for this power series representation? (e) Indicate how you would find a power series representation of f(x) centered at e, c an arbitrary real number. Are there any real numbers that cannot be used for c? Explain.

Q: part d please in the original picture!

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Q: Let Mbe as in Equation (3.14) and let X = [1, 0, ½]¹. Show that the entries of Y=MX sum to 1.

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.