Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 9 3x + 2 , c = 6

The interval of convergence is:

Step-by-step explanation:

Given

The geometric series centered at c is of the form:

Where:

first term

common ratio

We have to write

In the following form:

So, we have:

Rewrite as:

Factorize

Open bracket

Rewrite as:

Collect like terms

Take LCM

So, we have:

By comparison with:

At c = 6, we have:

Take LCM

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)

So, the power series becomes:

Substitute 1 for a

Substitute the expression for r

Expand

Further expand:

The power series converges when:

Multiply both sides by 3

Expand the absolute inequality

Solve for x

Take LCM

The interval of convergence is:

im here

step-by-step explanation:

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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