Lets x is the labor charges per hour
3x + 126.53 = 220.28
3x = 220.28 - 126.53
3x = 93.75
x = 93.75 / 3
x = 31.25
answer: $31.25 per hour charged for labor
Answer:
![\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}=-1/36](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B6%2Bx%7D-%5Cfrac%7B1%7D%7B6%7D%7D%7Bx%7D%3D-1%2F36)
Step-by-step explanation:
So we have the limit:
![\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B6%2Bx%7D-%5Cfrac%7B1%7D%7B6%7D%7D%7Bx%7D)
Let's remove the fractions in the denominator by multiplying both layers by (6+x)(6). So:
![\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}\cdot (\frac{(6+x)(6)}{(6+x)(6)})](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B6%2Bx%7D-%5Cfrac%7B1%7D%7B6%7D%7D%7Bx%7D%5Ccdot%20%28%5Cfrac%7B%286%2Bx%29%286%29%7D%7B%286%2Bx%29%286%29%7D%29)
Distribute:
![=\lim_{x \to 0} \frac{(6)-(6+x)}{x(6+x)(6)}](https://tex.z-dn.net/?f=%3D%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%286%29-%286%2Bx%29%7D%7Bx%286%2Bx%29%286%29%7D)
Simplify the numerator:
![=\lim_{x \to 0} \frac{6-6-x}{x(6+x)(6)}\\=\lim_{x \to 0} \frac{-x}{x(6+x)(6)}](https://tex.z-dn.net/?f=%3D%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B6-6-x%7D%7Bx%286%2Bx%29%286%29%7D%5C%5C%3D%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B-x%7D%7Bx%286%2Bx%29%286%29%7D)
Both the numerator and the denominator have an x. Cancel:
![=\lim_{x \to 0} \frac{-1}{(6+x)(6)}](https://tex.z-dn.net/?f=%3D%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B-1%7D%7B%286%2Bx%29%286%29%7D)
Direct substitution:
![= \frac{-1}{(6+0)(6)}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B-1%7D%7B%286%2B0%29%286%29%7D)
Simplify:
![=-1/36](https://tex.z-dn.net/?f=%3D-1%2F36)
And that's our answer.
And we're done!
Answer:
3
Step-by-step explanation:
Just so you know, there's no diagram