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Determine the infinite limit.

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

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Missouri State University

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

to evaluate this limit, know that we can rewrite this into limit as X approaches three from the left of square the vex times we have limits as X approaches three from the left of one over x minus three, race to the fifth power. Now from here we have the square root of three times limit as X approaches three from the left of one over x minus three to the fifth power. And from here, if X approaches three from the left, then that means that X values are less than three or that's X less than three. And this would tell us that x minus three is less than zero or the value of x minus three is negative. And so approaching three from the left would tell us that x minus three is a small negative number and becomes even smaller when raised to the fifth power. And so one over the fifth power of x minus three becomes a very large negative number. And so this is just square root of three times in negative infinity, which is the same as negative infinity. And so the value of the limit will be negative infinity.