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Determine the infinite limit.

$ \displaystyle \lim_{x \to 3^-}\frac{\sqrt{x}}{(x-3)^5} $

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Harvey Mudd College

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Boston College

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This is Problem number thirty four of Stuart. A tradition Section two point two determined the infinite element. The limit has X purchased three from the left. The square root of X, divided by the quantity explains three to the fifth power. We're going to begin by estimating this, and we're going to use the number smaller than three. Were very close to three for the numerator. A number of very, very close to three. Well, just estimate is three for the numerator, since there is no issue here, The denominator there is an issue. There's a challenge with using three in Ramos three because then we have zero in the denominator. That's not possible. That leaves us tonight to find a solution using a value very close. A three, such as it's a point nine nine. Well, give us something like two point in and minus three. Cora about negative, his heir point zero one. This is an example, showing that a very close number two three results in a very small negative number. We can extend this further and say that overall, her limit is going to be defined by approximately the square root of three divided by a very small little number to the fifth power, which is a very small negative number. This representing a number to the left of zero very, very close to zero. And if this is a very small negative number and the numerator zari or the numerator is a fine my positive number, this will always result and and you have infinite. If we take any friend, remember and we divide a very, very, very small number we get infinity If we divide a very, very small negative number, we have negative committee and this is thie independent limit shown here as exit purchased three from the left for this function using a graft to confirm we have graft function here around the value X equals three and we see that we hear the function and that comes from the left towards three approach of negative infinity

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