I instantly thought "you cant divide by zero" So, at some point that was drilled into my head by a teacher, so it should be undefined or not able to be solved. I believe that's why a calculator shows 'error' when you divide a number by zero.
X/0 means zero multiplies by what to get X? Well, zero multiplies by any number is still zero, that is why X/0 is undefined.
Taking a limit is not a branch of calculus. Taking a limit is taking a limit. The limit of 1/X as x approaches 0 is basically asking what happens to the function f(x)=1/x as x approaches 0. The function approaches infinity. It isn't the same as 1/0. Another example is x/x as x->inf. The function is not defined but the limit approaches 1.
1/0 is undefined... 0/0 is not undefined, it's indeterminate .... enter l'Hopital and limits ... or at least that's what I remember from all that math I never ended up using :grin:
x cannot be determined in this problem. Btw, this reminds me of the classic proof that one equals two: http://www.math.toronto.edu/mathnet/falseProofs/first1eq2.html
I guess I always think of these questions and certain elements of math as useless. No offense to the OP, but when does anyone need to know this unless they work with software or teach math? What is the point of it all? I've never been a "math brain," so maybe I'm wrong, but it just seems so minimal in terms of importance. Flame away if I offended you.
I understand what you're saying, but applying that line of thought to 90% of the things we do leads us to conclude that a bunch of crap we know or do is useless. I mean seriously, who gives a damn if you know what happened on Duck Dynasty last night? So you know who has thrown for the most touchdowns in Houston Oiler history - big deal. So you're an expert on road bikes ... wooptie damn doo. Until you find those people with a common interest and then you realize why we give a damn about pointless crap... you're just human. lol.
The original problem isn't well-defined as the specified range isn't represented by the equation. (Easier math) Consider this example: xy = 1 (what is x when y=0? what is y when x=0?) x = 1/y y = 1/x These are all the same equation. If you graph it, the curve is asymptotic in behavior; follow x as far as you want in the positive or the negative direction, it will never cross y=0; it will also never cross x=0. The curve is called undefined at these points because it never touches them. (Harder math) Messing with y = z - x/y in the same way: y(z-y)/x = 1 At first glance, it seems the same as the above equation and one would guess that when y=0 or (z-y)=0 that this equation is undefined. But second glance, if y(z-y) = x, then you can get 1. As some posters have already mentioned, for y(z-y)/x = 1, you could get 0/x =1 (x not equal to 0, undefined) or 0/0=1. The equation is indeterminate and may either cross or not cross at that point in which you use other tools to figure it out (L'Hopital's, etc.). On the math being useless topic - every discipline or topic can train your brain, make you a more well-rounded person, and has concepts that can be applied elsewhere. Chemistry: - Slow step of the reaction determines the rate (driving, speeding on the highway doesn't make as much sense as hustling in slow areas). - Like dissolves like (negotiation, if you want to get something across to someone, use tactics that they endear the most) History: - History is dependent on the writer (if you want the full story, get multiple perspectives) - Mistakes are repeated; mistakes punctuate events as much as deliberation. Music: - Silent points determine melody and rhythm as much as notes (background can have as much effect as foreground). - What someone considers harmony is dependent on their conditioning (cultural relativity). Math - An equation represents two equivalent values and an operation done to both sides doesn't affect the equality (recognizing equal/inequal things and how to change them). - Finding the value of a variable (identifying an unknown, and using all kinds of methods to find its value). If anything, math has the most conceptual, mental training of any subject - induction, balance, considering extremes or the upside down to solve things, logic, spatial reasoning, and so much more. Practically, it will teach you to save money at the store, help you mount your TV, not rely on others and get screwed wherever finances or numbers are involved... I'm sorry if it sounds condescending but I just feel plain bad for someone who thinks math has little use in their lives. It's one of the most enriching things widely available to humans and I wish that person had a better math teacher growing up to teach them that. Ok, my sermons done. Back to boob and sports threads.
Sub. would be: 0 = 0 - x/0 So, x/0 has to equal 0. You cant say 0=undefined, obviously. so, for x/0 to equal 0, x needs to be 0. ps, I just owned the gmat, this question would be an easy question.
Before we can discuss this everyone has to accept that the number zero is just a theory. And that's a fact. Pun intended For instance, what is any number to the zero power. Now, tell me what zero to the zero power is. It's a big debate
Indeterminado! You can use L'Hopital's Rule here but haven't seen the guy since college and never did like the French. Trust me I'm an engineer.
