determine-the-infinite-limit-displaystyle-lim_x-to-3-fracsqrtxx-35

Question

Determine the infinite limit.

$ \displaystyle \lim_{x 	o 3^-}\frac{\sqrt{x}}{(x-3)^5} $

Daniel Jaimes · Accepted Answer

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&#x27;re going to begin by estimating this, and we&#x27;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&#x27;s a challenge with using three in Ramos three because then we have zero in the denominator. That&#x27;s not possible. That leaves us tonight to find a solution using a value very close. A three, such as it&#x27;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

Problem

Determine the infinite limit. $ \displaystyle …

Problem 34 Easy Difficulty

Determine the infinite limit.

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

Answer

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