Finding Power Series Representation of Derivatives: 1/x-9

In summary, to find a power series representation of d/dx (1/x-9), you can calculate the Taylor series around a chosen point (a=0 would be easiest) by finding derivatives up to the nth derivative and substituting them into the general series. Considering the expression as -1/9 * d/dx (1/(1-x/9)), you can use the geometric series method to find the representation.
  • #1
sportlover36
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how can i find a power series representaion of d/dx (1/x-9)
 
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  • #2
You can find an approximation by calculating the Taylor series around some point (a=0 would probably be easiest). All you need to do is find derivatives of the function up to the nth derivative, depending on how accurate you want the representation to be, and substitute them into the general series given http://en.wikipedia.org/wiki/Taylor_series" .
 
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  • #3
sportlover36 said:
how can i find a power series representaion of d/dx (1/x-9)
It looks like you may have some sort of a typo. At x=0, 1/x is infinite.
 
  • #4
I mean for it to say d/dx (1/(x-9)) sorrry
 
  • #5
sportlover36 said:
how can i find a power series representaion of d/dx (1/x-9)

This expression can be written as -1/9 * d/dx (1/(1-x/9)). Then think geometric series. Can you see it from there?
 

FAQ: Finding Power Series Representation of Derivatives: 1/x-9

What is a power series representation?

A power series representation is a series of terms that can be used to approximate a function. It takes the form of ∑n=0∞ancn, where a is a constant and c is the degree of the term.

How do you find the power series representation of a function?

To find the power series representation of a function, you need to find the coefficients a and c for each term in the series. This can be done using the Taylor series expansion, which involves taking derivatives of the function at a specific point and plugging them into the formula.

What is the power series representation of 1/x-9?

The power series representation of 1/x-9 is ∑n=0∞9^n/x^(n+1). This can be found by using the Taylor series expansion for 1/x-9 at a specific point, such as x=0.

Why is it useful to find the power series representation of a function?

Finding the power series representation of a function allows us to approximate the function and make calculations easier. It also allows us to analyze the behavior of the function and understand its properties.

What are some applications of power series representations?

Power series representations have many applications in mathematics, physics, and engineering. They are commonly used in calculus to approximate functions and solve problems. They are also used in fields such as signal processing, circuit analysis, and statistics.

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