Discuss what happens to the value of the function f(x)=1/x as x approaches infinity

  • Thread starter Thread starter Kyle
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Think about fractions of increasingly large denominators: the larger the denominator gets, the "smaller" the number gets...

1/2 = 0.5
1/4 = 0.25
1/10 = 0.1
1/100 = 0.01
1/100000 = 0.00001
etc.

Now, "smaller" is in quotation marks because the number doesn't just get smaller in the strictest sense of the word. The number actually gets closer to zero. So, as the denominators gets larger (i.e., as x gets gets closer to infinity), the number (1/x) gets closer to zero.

Now lets examine what happens when you divide by larger and larger negative numbers...

1/(-2) = -0.5
1/(-4) = -0.25
1/(-100) = -0.01
1/(-100000) = -0.00001
etc.

We see a similar pattern. The numbers get closer to zero; the difference is that here we're approaching zero from "below", whereas before we were approaching zero from "above". So, the conclusion we draw is that as x (the denominator) approaches negative infinity, 1/x approaches zero.
 
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