Limit question - It makes sense to me why the limit as x tends to 4 of 1/(x-4) is undefined. What I don't understand is why the same limit of 1/(x-4)^2 tends to infinity. Could someone explain this.

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Limit question - It makes sense to me why the limit as x tends to 4 of 1/(x-4) is undefined. What I don't understand is why the same limit of 1/(x-4)^2 tends to infinity. Could someone explain this.

OCW Scholar - Single Variable Calculus
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Check out both graphs. One fundamental requirement for a limit to exist is that the limit from the left must equal the limit from the right. If you look at your first function, the limit from the left is negative infinity while the limit from the right is positive infinity. For the second function that you mention, the limit from the left and the limit from the right both approach positive infinity at the exact same rate.
if you pick a point that is a given distance to the left of x=4 and the same distance to the right of 4, the y-values will be the same. So the limit from the left will alway equal the limit from the right... which is all that you need.
Abundantly clear now. Thank you.

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