Help with problem

[jlind]

(08-04-2019 06:50 PM)levi98 Wrote:  

Using hp prime
need help

I took one look at this and realized the answer is A, and I'm with the several others who stated that X cannot be +5 or -5. Either value makes the denominator zero. When graphed by hand, it's clear that y becomes great without bound when:
x --> -5
y is therefore undefined if x = -5, as it's a real number (-10) divided by zero. The graph shows y becomes great in the negative direction as x --> -5 from less than -5 (e.g. -5.11), and it gets great in the positive direction as x --> -5 from larger than -5 (e.g. -4.99). The principle being demonstrated here is why, by definition, any number (including 0) that's divided by 0 is undefined. The direction in which it's great without bound, + or -, is indeterminate. It cannot be both simultaneously.

There must also be a hole shown where x = 5, as it creates a denominator with the original quadratic that goes to zero. By definition, 0 divided by any number other than 0 is zero. Zero divided by zero, just like any other real number divided by zero, is also undefined. In other words, 0/0 is not equal to one. I believe that's the underlying principle here. At the limit where x --> 5, y --> 0.1, but that's not the same as x = 5. Plug in x = 5.1 and 5.01, and then x = 4.9 and 4.99 to see what you get. It converges on each side of 0.1 and there's an infinitesimally tiny hole for exactly x = 5. Zero is a special case that is neither a positive nor a negative real number. It has no "sign" like all other real numbers. Hope this explains some of the underlying principles surrounding why division of any real number, including zero, by zero is undefined.

John