Assuming "root 9 of n" is supposed to mean "the ninth root of n", that is
![\sqrt[9]n](https://tex.z-dn.net/?f=%5Csqrt%5B9%5Dn)
we can use the ratio test, which says the series converges whenever
![\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{\sqrt[9]{n+1}}}{\frac{x^n}{\sqrt[9]n}}\right|](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cleft%7C%5Cfrac%7B%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7B%5Csqrt%5B9%5D%7Bn%2B1%7D%7D%7D%7B%5Cfrac%7Bx%5En%7D%7B%5Csqrt%5B9%5Dn%7D%7D%5Cright%7C%3C1)
We have
![\displaystyle|x|\lim_{n\to\infty}\frac{\sqrt[9]n}{\sqrt[9]{n+1}}=|x|\sqrt[9]{\lim_{n\to\infty}\frac n{n+1}}=|x|](https://tex.z-dn.net/?f=%5Cdisplaystyle%7Cx%7C%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac%7B%5Csqrt%5B9%5Dn%7D%7B%5Csqrt%5B9%5D%7Bn%2B1%7D%7D%3D%7Cx%7C%5Csqrt%5B9%5D%7B%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac%20n%7Bn%2B1%7D%7D%3D%7Cx%7C%3C1)
which means the radius of convergence for this power series is 1.
<span>e4 + -1.875r2 + 0.875x-1 = 0.000</span>
<span>Let g(x) = f(x) - 4
g(x) is a translation of f(x) down 4 units so (-3, 1) will be the new point
find g(-3)
g(-3) = f(-3) - 4
= 5 - 4
= 1
hope this helps</span>
a. There's a restaurant that charges $35 just to get inside plus $2.50 per hour.
b. The rate of change is 2.5. The meaning is each hour you're in the restaurant, they charge you $2.50.
