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How do you find the limit of #(4^y) / (y^2)# as y approaches 0?

Answer 1

#lim_(y->0) (4^y)/y^2 = +oo#

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples. (From: https://tutor.hix.ai) Many more details, and a good video there too.

In this case the controlling factor is the denominator. No matter what path the numerator takes, the ratio must approach #+oo# as #y -> 0#

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Answer 2

Charles Arocha

To find the limit of (4^y) / (y^2) as y approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (ln(4) * 4^y) / (2y). Evaluating this expression as y approaches 0, we have (ln(4) * 4^0) / (2 * 0), which simplifies to ln(4) / 0. Since ln(4) is a constant, the limit is undefined.

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Answer from HIX Tutor