Answer:
A
Step-by-step explanation:
We are given the function:
And we want to find:
So, we need to determine whether or not the limit exists. In other words, we will find the two one-sided limits.
Left-Hand Limit:
Since we are approaching from the left, we will use the first equation:
By direct substitution:
Right-Hand Limit:
Since we are approaching from the right, we will use the second equation:
Direct substitution:
So, we can see that:
Since both the left- and right-hand limits exist and equal the same thing, we can conclude that:
Our answer is A.
Answer:
108 108 108 108 and 35
Step-by-step explanation:
108 108 108 108 and brain and five stars OR ELSE jk. I think it's 35?
You can rewrite the equation in vertex form to find some of the parameters of interest.
x² +8x +4 = -4y
x² +8x +16 -12 = -4y
(x+4)² -12 = -4y
y = (-1/4)(x +4)² +3
From this, we see
the vertex is (-4, 3).
The scale factor, (-1/4) is 1/(4p), where p is the distance from the vertex to the focus. Solving for p, we have
-1/4 = 1/(4p)
p = -1 . . . . . multiply by -4p
So, the focus is 1 unit below the vertex.
The focus is (-4, 2).
The directrix is the same distance from the vertex, but in the opposite direction, hence
the directrix is y = 4.
_____
On a graph, if all you know is the vertex, you can draw a line with slope 1/2 through the vertex. It intersects the parabola at the y-value of the focus. Then the distance from that point of intersection to the axis of symmetry (where the focus lies) is the same as the distance from that point to the directrix.
Every point on the parabola, including the vertex and the point of intersection just described, is the same distance from the focus and the directrix. This point of intersection is on a horizontal line through the focus, so finding the distance is made easy.
I think that the answer is €192
Answer:
x<-1
Step-by-step explanation:
All of the numbers on/in the set are below -1. That means for that any of them to be x, the inequality would be x<-1.
