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Negative Infinity

What’s the fastest way that you could help this student?

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3 replies on “Negative Infinity”

Another student was complaining to me recently how teachers don’t like when he writes E rather than x10^. Do you think writing this in scientific notation would have helped or would the student still breeze by the negative sign?

l hodgesays:

Actually beginning to evaluate by hand helps to show both the value of the limit and why the larger exponents run the show in this case. Plug 1000 in for x:

Numerator: 5,000,000 – 12

Denominator: 1,000,000,000,000 + 5,000,000

Most will probably have enough sense of place value to realize this is pretty much the same as 5,000,000/1,000,000,000,000. May not be a slam dunk for everyone that this is close to 0.

x^2 & x^4 look pretty similar, as do 1000^2 & 1000^4, and very large or small numbers that the calculator spits out in scientific notation.

It seems like a lot of kids don’t really understand what their calculators mean when they say “E-12” or whatnot. I always hope that making kids write the exponent of 10 will help them have a little more chance to understand the meaning, but I don’t know that I have any evidence that this policy actually helps. It’s more of a case of me not knowing what else to do when I have kids who don’t know what their calculator’s display is telling them.

I think my approach here, though, would be more algebraic: “When x is really big, the highest power of x totally blows away the other powers in a sum” to get them to (5x^2)/(x^4) and then to 5/x^2 and then to “5 divided by a really big number is practically zero”. So I don’t know how much, in helping this kid, I’d focus on that kind of understanding of limits as opposed to working on getting them to understand “E-12”.

The misuse of “=” here always irritates me a bit, too. I wish I had some better idea of how to get kids to use some other symbol when they mean some other relationship.