Answer:
The general limit exists at <em>x</em> = 9 and is equal to 300.
Step-by-step explanation:
We want to find the general limit of the function:
![\displaystyle \lim_{x \to 9}(x^2+2^7+(9.1\times 10))](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29)
By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.
So, let's find each one-sided limit: the left-hand side and the right-hand side.
The left-hand limit is given by:
<h3>
![\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E-%7D%28x%5E2%2B2%5E7%2B%289.1%20%5Ctimes%2010%29%29)
</h3>
Since the given function is a polynomial, we can use direct substitution. This yields:
![=(9)^2+2^7+(9.1\times 10)](https://tex.z-dn.net/?f=%3D%289%29%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29)
Evaluate:
![300](https://tex.z-dn.net/?f=300)
Therefore:
![\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))=300](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E-%7D%28x%5E2%2B2%5E7%2B%289.1%20%5Ctimes%2010%29%29%3D300)
The right-hand limit is given by:
![\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E%2B%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29)
Again, since the function is a polynomial, we can use direct substitution. This yields:
![=(9)^2+2^7+(9.1\times 10)](https://tex.z-dn.net/?f=%3D%289%29%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29)
Evaluate:
![=300](https://tex.z-dn.net/?f=%3D300)
Therefore:
![\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E%2B%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29%3D300)
Thus, we can see that:
![\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1\times 10))=\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E-%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29%3D%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E%2B%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29%3D300)
Since the two-sided limits exist and are equivalent, the general limit of the function does exist at <em>x</em> = 9 and is equal to 300.
You have to convert all terms to inches so that they are all like terms, there are 12 inches in a foot so you multiply everything by 12. You dont multiply the 10 inches though because its already in inches
6x12=72 8x12=96 2x12=24
Then you multiply to find the areas of the large shape. It was the 6ft and 8ft so you multiply the 72 and 96
72x96=6912
Then you multiply to find the smaller shape. It was the 2 and 10 so do 24 times 10.
24 x 10= 240
then you divide 240 by 12 to get to the feet so it
240/12 = 20ft
And that equals 9.5 you always put a .5 next to 9 or any other number. Or, if you're doing a question that has to equal a number of candy in every bag, or something else, you add the remainder as the number 1 with 9. So 1+9 =10 either one of those:)
The side that corresponds with side AB is side DE