X=14
2x=28
4x-9=47
you solve for x after you add all the sides
Answer:
d) The limit does not exist
General Formulas and Concepts:
<u>Calculus</u>
Limits
- Right-Side Limit:
![\displaystyle \lim_{x \to c^+} f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%20c%5E%2B%7D%20f%28x%29)
- Left-Side Limit:
![\displaystyle \lim_{x \to c^-} f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%20c%5E-%7D%20f%28x%29)
Limit Rule [Variable Direct Substitution]: ![\displaystyle \lim_{x \to c} x = c](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20x%20%3D%20c)
Limit Property [Addition/Subtraction]: ![\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20%5Bf%28x%29%20%5Cpm%20g%28x%29%5D%20%3D%20%20%5Clim_%7Bx%20%5Cto%20c%7D%20f%28x%29%20%5Cpm%20%5Clim_%7Bx%20%5Cto%20c%7D%20g%28x%29)
Step-by-step explanation:
*Note:
In order for a limit to exist, the right-side and left-side limits must equal each other.
<u>Step 1: Define</u>
<em>Identify</em>
![\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D5%20-%20x%2C%5C%20x%20%3C%205%5C%5C8%2C%5C%20x%20%3D%205%5C%5Cx%20%2B%203%2C%5C%20x%20%3E%205%5Cend%7Barray%7D)
<u>Step 2: Find Right-Side Limit</u>
- Substitute in function [Limit]:
![\displaystyle \lim_{x \to 5^+} 5 - x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%205%5E%2B%7D%205%20-%20x)
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
![\displaystyle \lim_{x \to 5^+} 5 - x = 5 - 5 = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%205%5E%2B%7D%205%20-%20x%20%3D%205%20-%205%20%3D%200)
<u>Step 3: Find Left-Side Limit</u>
- Substitute in function [Limit]:
![\displaystyle \lim_{x \to 5^-} x + 3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%205%5E-%7D%20x%20%2B%203)
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
![\displaystyle \lim_{x \to 5^+} x + 3 = 5 + 3 = 8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%205%5E%2B%7D%20x%20%2B%203%20%3D%205%20%2B%203%20%3D%208)
∴ Since
, then ![\displaystyle \lim_{x \to 5} f(x) = DNE](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%205%7D%20f%28x%29%20%3D%20DNE)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
If 2 ounces = 240 calories
1 ounce = 120 calories
So 2/3 ounces = (2/3) * 120
= 80 calories
The isosceles triangle is missing so i have attached it.
Answer:
Length of unknown side = 5p + 6
Step-by-step explanation:
In isosceles triangle, two of the sides are equal. In the attached triangle, we see that one of the equal sides is given as 5p + 3.
Thus,the second equal side is also 5p + 3.
Now, perimeter of a triangle is the sum of the three sides.
We have two sides and let the third side be denoted as x.
Thus;
Perimeter = (5p + 3) + (5p + 3) + x
We are given perimeter = 15p + 12
Thus;
(5p + 3) + (5p + 3) + x = 15p + 12
10p + 6 + x = 15p + 12
Rearranging, we have;
x = 15p - 10p + 12 - 6
x = 5p + 6
The operator
is transitive, which means exactly that
![x \geq y,\quad y\geq z \implies x \geq z](https://tex.z-dn.net/?f=x%20%5Cgeq%20y%2C%5Cquad%20y%5Cgeq%20z%20%5Cimplies%20x%20%5Cgeq%20z)
That's the only thing you can deduce from your statement.