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Problem 40 Medium Difficulty

Determine the infinite limit.

$ \displaystyle \lim_{x \to 2^-}\frac{x^2 - 2x}{x^2 - 4x + 4} $

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Video Transcript

to evaluate the limits of x squared minus two. X over x squared minus four, X plus four. As X approaches to from the left, we would rewrite this into the limit as X approaches to from the left of X Times X -2. This all over X -2 Squared. And then from here we can simplify, we can get rid of x minus two and we have Limit as X approaches to from the left of X over we still have X -2 in the denominator. Now, if we plug in two to this function we have to over 2 -2, that's two over zero. Now, if X approaches to from the left then the values of X we are looking at are those X values less than two. So if X is less than two, this means that X -2 will be less than zero. That means The value of X -2 as X approaches to from the left would be a small negative number And so the value of X over X -2 would be a negative infinite number. Therefore this is equal to negative infinity.