Answer:
![(\frac{a^{2}b^{-3} }{a^{-2}b^{2} })^{2} = (a^{2-(-2) }b^{-3 - 2})^{2} \\ = (a^{4}b^{-5} )^{2} = (a^{4})^{2} (b^{-5})^{2} = a^{8} b^{-10}](https://tex.z-dn.net/?f=%28%5Cfrac%7Ba%5E%7B2%7Db%5E%7B-3%7D%20%20%7D%7Ba%5E%7B-2%7Db%5E%7B2%7D%20%20%7D%29%5E%7B2%7D%20%20%3D%20%28a%5E%7B2-%28-2%29%20%7Db%5E%7B-3%20-%202%7D%29%5E%7B2%7D%20%5C%5C%20%3D%20%28a%5E%7B4%7Db%5E%7B-5%7D%20%29%5E%7B2%7D%20%20%3D%20%28a%5E%7B4%7D%29%5E%7B2%7D%20%28b%5E%7B-5%7D%29%5E%7B2%7D%20%20%3D%20a%5E%7B8%7D%20%20b%5E%7B-10%7D)
Here is for you.
Step-by-step explanation:
We know is a semi-circle, so let us use the equation for the area of a circle instead, and then, half it
so, the diameter is 1100, meaning the radius is half that, or 550
so...
The power series for given function
is
For given question,
We have been given a function g(x) = 4x / (x² + 2x - 3)
We need to find a power series for the function, centered at c, for c = 0.
First we factorize the denominator of function g(x), we have:
![\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}](https://tex.z-dn.net/?f=%5CRightarrow%20g%28x%29%3D%5Cfrac%7B4x%7D%7B%28x-1%29%28x%2B3%29%7D)
We can write g(x) as,
![\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\](https://tex.z-dn.net/?f=%5CRightarrow%20g%28x%29%3D%5Cfrac%7B1%7D%7Bx-1%7D%2B%5Cfrac%7B3%7D%7Bx%2B3%7D%5C%5C%5C%5C%5CRightarrow%20g%28x%29%3D%5Cfrac%7B-1%7D%7B1-x%7D%2B%5Cfrac%7B1%7D%7B1%2B%5Cfrac%7Bx%7D%7B3%7D%20%7D%5C%5C%5C%5C%5CRightarrow%20g%28x%29%3D%5Cfrac%7B-1%7D%7B1-x%7D%2B%5Cfrac%7B1%7D%7B1-%28-%5Cfrac%7Bx%7D%7B3%7D%20%29%7D%5C%5C)
We know that,
if |x| < 1
and
if ![|\frac{x}{6}| < 1](https://tex.z-dn.net/?f=%7C%5Cfrac%7Bx%7D%7B6%7D%7C%20%3C%201)
if |x| < 1 and if ![|\frac{x}{6}| < 1](https://tex.z-dn.net/?f=%7C%5Cfrac%7Bx%7D%7B6%7D%7C%20%3C%201)
if |x| < 1
Therefore, the power series for given function
is
Learn more about the power series here:
brainly.com/question/11606956
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Since -4 is less than 2, use the first equation
5(-4) - 1 = -20 - 1 = -21