Ayy you got it right thank you very much your
Answer:
d. does not exist
Step-by-step explanation:
The given limits are;
,
and ![\lim_{x \to 4} h(x) =-2](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%204%7D%20h%28x%29%20%3D-2)
We want to find
![\lim_{x \to 4} \frac{f}{g}(x)= \lim_{x \to 4} \frac{f(x)}{g(x)}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%204%7D%20%5Cfrac%7Bf%7D%7Bg%7D%28x%29%3D%20%5Clim_%7Bx%20%5Cto%204%7D%20%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D)
By the properties of limits, we have;
![\lim_{x \to 4} \frac{f}{g}(x)= \frac{\lim_{x \to 4} f(x)}{\lim_{x \to 4} g(x)}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%204%7D%20%5Cfrac%7Bf%7D%7Bg%7D%28x%29%3D%20%5Cfrac%7B%5Clim_%7Bx%20%5Cto%204%7D%20f%28x%29%7D%7B%5Clim_%7Bx%20%5Cto%204%7D%20g%28x%29%7D)
This gives us;
![\lim_{x \to 4} \frac{f}{g}(x)= \frac{5}{0}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%204%7D%20%5Cfrac%7Bf%7D%7Bg%7D%28x%29%3D%20%5Cfrac%7B5%7D%7B0%7D)
Division by zero is not possible. Therefore the limit does not exist.
If you didn't change the slope of the line, but you moved it
down 6 units on the graph, then its y-intercept would become
6 less. The equation of the new line would be ...
y = 1/3 x - 16 .
first off, let's notice the parabola is a vertical one, therefore the squared variable is the x, and the parabola is opening upwards, meaning the coefficient of x² is positive.
let's notice the vertex, or U-turn, is at (-2, 2)
![\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \boxed{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{-2}{ h},\stackrel{2}{ k}) \\\\\\ y=+1[x-(-2)]^2+2\implies y=(x+2)^2+2](https://tex.z-dn.net/?f=%20%5Cbf%20~~~~~~%5Ctextit%7Bparabola%20vertex%20form%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5Cboxed%7By%3Da%28x-%20h%29%5E2%2B%20k%7D%5C%5C%5C%5C%20x%3Da%28y-%20k%29%5E2%2B%20h%20%5Cend%7Barray%7D%20%5Cqquad%5Cqquad%20vertex~~%28%5Cstackrel%7B-2%7D%7B%20h%7D%2C%5Cstackrel%7B2%7D%7B%20k%7D%29%20%5C%5C%5C%5C%5C%5C%20y%3D%2B1%5Bx-%28-2%29%5D%5E2%2B2%5Cimplies%20y%3D%28x%2B2%29%5E2%2B2%20)
6√5 - 4√3-
i took the test but sorry if its wrong