Answer:
(1,-1)
Step-by-step explanation:
A. If you fail to pay your cell phone bill, your cell provider may cut your service. You may have debt and your contract will be canceled.
B. If you fail to pay your credit card bill on time, you will have to pay late fees, receive increased interest rates, and incur damages to your credit score. If you continue to miss payments your card can be frozen, your debt could be sold to a collection agency, and the owner of your debt could sue you and have your salary garnished.
Answer:
31
Step-by-step explanation:
u divide 186 by 6. u divide by pretty much seeing how many times 6 can go into 186.
A. Factor the numerator as a difference of squares:
![\displaystyle\lim_{x\to9}\frac{x-9}{\sqrt x-3}=\lim_{x\to9}\frac{(\sqrt x-3)(\sqrt x+3)}{\sqrt x-3}=\lim_{x\to9}(\sqrt x+3)=6](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto9%7D%5Cfrac%7Bx-9%7D%7B%5Csqrt%20x-3%7D%3D%5Clim_%7Bx%5Cto9%7D%5Cfrac%7B%28%5Csqrt%20x-3%29%28%5Csqrt%20x%2B3%29%7D%7B%5Csqrt%20x-3%7D%3D%5Clim_%7Bx%5Cto9%7D%28%5Csqrt%20x%2B3%29%3D6)
c. As
![x\to\infty](https://tex.z-dn.net/?f=x%5Cto%5Cinfty)
, the contribution of the terms of degree less than 2 becomes negligible, which means we can write
![\displaystyle\lim_{x\to\infty}\frac{4x^2-4x-8}{x^2-9}=\lim_{x\to\infty}\frac{4x^2}{x^2}=\lim_{x\to\infty}4=4](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%5Cinfty%7D%5Cfrac%7B4x%5E2-4x-8%7D%7Bx%5E2-9%7D%3D%5Clim_%7Bx%5Cto%5Cinfty%7D%5Cfrac%7B4x%5E2%7D%7Bx%5E2%7D%3D%5Clim_%7Bx%5Cto%5Cinfty%7D4%3D4)
e. Let's first rewrite the root terms with rational exponents:
![\displaystyle\lim_{x\to1}\frac{\sqrt[3]x-x}{\sqrt x-x}=\lim_{x\to1}\frac{x^{1/3}-x}{x^{1/2}-x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto1%7D%5Cfrac%7B%5Csqrt%5B3%5Dx-x%7D%7B%5Csqrt%20x-x%7D%3D%5Clim_%7Bx%5Cto1%7D%5Cfrac%7Bx%5E%7B1%2F3%7D-x%7D%7Bx%5E%7B1%2F2%7D-x%7D)
Next we rationalize the numerator and denominator. We do so by recalling
![(a-b)(a+b)=a^2-b^2](https://tex.z-dn.net/?f=%28a-b%29%28a%2Bb%29%3Da%5E2-b%5E2)
![(a-b)(a^2+ab+b^2)=a^3-b^3](https://tex.z-dn.net/?f=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%3Da%5E3-b%5E3)
In particular,
![(x^{1/3}-x)(x^{2/3}+x^{4/3}+x^2)=x-x^3](https://tex.z-dn.net/?f=%28x%5E%7B1%2F3%7D-x%29%28x%5E%7B2%2F3%7D%2Bx%5E%7B4%2F3%7D%2Bx%5E2%29%3Dx-x%5E3)
![(x^{1/2}-x)(x^{1/2}+x)=x-x^2](https://tex.z-dn.net/?f=%28x%5E%7B1%2F2%7D-x%29%28x%5E%7B1%2F2%7D%2Bx%29%3Dx-x%5E2)
so we have
![\displaystyle\lim_{x\to1}\frac{x^{1/3}-x}{x^{1/2}-x}\cdot\frac{x^{2/3}+x^{4/3}+x^2}{x^{2/3}+x^{4/3}+x^2}\cdot\frac{x^{1/2}+x}{x^{1/2}+x}=\lim_{x\to1}\frac{x-x^3}{x-x^2}\cdot\frac{x^{1/2}+x}{x^{2/3}+x^{4/3}+x^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto1%7D%5Cfrac%7Bx%5E%7B1%2F3%7D-x%7D%7Bx%5E%7B1%2F2%7D-x%7D%5Ccdot%5Cfrac%7Bx%5E%7B2%2F3%7D%2Bx%5E%7B4%2F3%7D%2Bx%5E2%7D%7Bx%5E%7B2%2F3%7D%2Bx%5E%7B4%2F3%7D%2Bx%5E2%7D%5Ccdot%5Cfrac%7Bx%5E%7B1%2F2%7D%2Bx%7D%7Bx%5E%7B1%2F2%7D%2Bx%7D%3D%5Clim_%7Bx%5Cto1%7D%5Cfrac%7Bx-x%5E3%7D%7Bx-x%5E2%7D%5Ccdot%5Cfrac%7Bx%5E%7B1%2F2%7D%2Bx%7D%7Bx%5E%7B2%2F3%7D%2Bx%5E%7B4%2F3%7D%2Bx%5E2%7D)
For
![x\neq0](https://tex.z-dn.net/?f=x%5Cneq0)
and
![x\neq1](https://tex.z-dn.net/?f=x%5Cneq1)
, we can simplify the first term:
![\dfrac{x-x^3}{x-x^2}=\dfrac{x(1-x^2)}{x(1-x)}=\dfrac{x(1-x)(1+x)}{x(1-x)}=1+x](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-x%5E3%7D%7Bx-x%5E2%7D%3D%5Cdfrac%7Bx%281-x%5E2%29%7D%7Bx%281-x%29%7D%3D%5Cdfrac%7Bx%281-x%29%281%2Bx%29%7D%7Bx%281-x%29%7D%3D1%2Bx)
So our limit becomes
So excluded values are x=3 and x=-2. Fully simplified form:
<span><span>1 over</span></span>
<span><span>x+2</span></span>