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Evaluate the limit, if it exists.

$ \displaystyle \lim_{u \to 2}\frac{\sqrt{4u + 1}-3}{u - 2} $

$\frac{2}{3}$

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Campbell University

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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there's a problem. Number twenty two of this tour catalyse a tradition section two point three. You know, they were filling it. If it exists, the limit is you were purchased two and quantity for you, plus one inside the square root minus three. They're right by the quantity you minus two. Whenever we have a problem of this horn, it helps to simplifying by multiplying the top and the bottom ninety. Conjure, get pair of this binomial you're gonna write as the pear and the consequence going right for you. Plus one under the radical plus three in the top and the bottom. And then we proceeded him while playing through. In order to start simplifying P square roots Cancel leaving you with that for you plus one the this radical plus three minus three times the same article. Jerry, this radical times three nine is three times same radical is zero. So those council minus three Time's a positive three minus nine. And that is the numerator. The denominator is just the two terms more deployed U minus two. Um, what's quite bright? This quandary for you, plus one in center radical. My name is plus three in the numerator. We can simplify a bit plus one minus trainer with minus eight. And in order for us to have it or tour our advantage in order and in terms of simplifying and reducing the fraction we take for you plus for you minus eight and factor out of four. And in the sense we get for times he minus two. And the best part of this is that in the denominator, we also happy you might miss, too. And we suspect that we can cancel East now, after having done that, we have foreign the numerator and then this conjugating on beginning and that not matter and we can proceed with her limit. Lim is your purchase, too. Or over square it for you plus one plus three and as you purchased. Two. The denominator coaches Square root of four times two plus one nine Fox three mrs Four on the numerator two out of three plus three. This being three it was three six and the simplifies to our solution off two or three

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