![f(x)=\begin{cases}5x-8&\text{for }x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cbegin%7Bcases%7D5x-8%26%5Ctext%7Bfor%20%7Dx%3C0%5C%5C%7C-4-x%7C%26%5Ctext%7Bfor%20%7Dx%5Cge0%5Cend%7Bcases%7D)
The limits from either side are
![\displaystyle\lim_{x\to0^-}f(x)=\lim_{x\to0}(5x-8)=-8](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto0%5E-%7Df%28x%29%3D%5Clim_%7Bx%5Cto0%7D%285x-8%29%3D-8)
![\displaystyle\lim_{x\to0^+}f(x)=\lim_{x\to0}|-4-x|=\lim_{x\to0}|x+4|=|4|=4](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto0%5E%2B%7Df%28x%29%3D%5Clim_%7Bx%5Cto0%7D%7C-4-x%7C%3D%5Clim_%7Bx%5Cto0%7D%7Cx%2B4%7C%3D%7C4%7C%3D4)
The one-sided limits don't match, so the limit as
does not exist.
Word form - six.seven
Expand form - 6 + 0.7
Answer: -0.7
Step-by-step explanation:
1 3/4 oz is mixed with 1 gallon of water. With 5 2/5 gallons of water, since we multiplied the number of gallons by 5 2/5, we multiply the amount of chemical by 5 2/5 as well:
1 3/4 * 5 2/5
Convert to improper fractions:
7/4 * 27/5 (because 1*4+3=7 and 5*5+2=27)
189/20 = 9 9/20 (because 20 goes into 189 9 times with 9 left over)
3 to the square root of 5
When we are multiplying the two numbers, we should notice that they share the same base. Because of this, we can add the exponents when we multiply them.