If a is an arbitrary nonzero constant, what happens to a/b as b approaches 0

Mathematics

1 answer:

Stolb23 [73]3 years ago

7 0

It depends on how b approaches 0

If b is positive and gets closer to zero, then we say b is approaching 0 from the right, or from the positive side. Let's say a = 1. The equation a/b turns into 1/b. Looking at a table of values, 1/b will steadily increase without bound as positive b values get closer to 0.

On the other side, if b is negative and gets closer to zero, then 1/b will be negative and those negative values will decrease without bound. So 1/b approaches negative infinity if we approach 0 on the left (or negative) side.

The graph of y = 1/x shows this. See the diagram below. Note the vertical asymptote at x = 0. The portion to the right of it has the curve go upward to positive infinity as x approaches 0. The curve to the left goes down to negative infinity as x approaches 0.

You might be interested in

Sasha is bisecting a segment. First, she places the compass on one endpoint, opens it to a width larger than half of the segment

ycow [4]

Her next step is to repeat the last process of drawing those two arcs. However, they will be mirrored since she swapped endpoints.

Check out the diagram below. Figure 1 is what she already has. Figure 2 is what happens after completing the next step. The red and blue arcs intersect to help form the endpoints of the perpendicular bisector. I used GeoGebra to make the diagrams.