The question is asking to choose among the following choices that states the question that represent the said sentence in your question and base on the fact and further understanding about the said sentence, I would say that the answer would be ((x+4)/2)-3(4/x). I hope you are satisfied with my answer and feel free to ask for more

8 0

3 years ago

Find the limit, if it exists, or type dne if it does not exist.

Phantasy [73]

$\displaystyle\lim_{(x,y)\to(0,0)}\frac{\left(x+23y)^2}{x^2+529y^2}$

Suppose we choose a path along the $x$ -axis, so that $y=0$ :

$\displaystyle\lim_{x\to0}\frac{x^2}{x^2}=\lim_{x\to0}1=1$

On the other hand, let's consider an arbitrary line through the origin, $y=kx$ :

$\displaystyle\lim_{x\to0}\frac{(x+23kx)^2}{x^2+529(kx)^2}=\lim_{x\to0}\frac{(23k+1)^2x^2}{(529k^2+1)x^2}=\lim_{x\to0}\frac{(23k+1)^2}{529k^2+1}=\dfrac{(23k+1)^2}{529k^2+1}$

The value of the limit then depends on $k$ , which means the limit is not the same across all possible paths toward the origin, and so the limit does not exist.

8 0

3 years ago

Y≤2x−3 y< -\frac{3}{4}x+8 y<− 4 3 ​ x+8

Y≤2x−3 y< -\frac{3}{4}x+8 y<− 4 3 x+8