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Determine the infinite limit.

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

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

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this is problem number forty Stuart Calculus. Safe addition. Section two point two Determined them. Connect Limit the limit. Hands ex purchased two from the left, uh, X squared minus two x divided by the quantity X squared minus for X plus four. Good first step is always to see if you can simplify the limited anyway, So we will go ahead and take some steps to simplifying this. This'LL emit dysfunction Well, first factor out of Nick's multiplied by Explain this to if we notice there's two of the same term able to play it on the top of the bottom. So we were able to survive Miss Lim as ex owner X minus two. Now, to find there a solution to this limit, you want to choose a value very close to two, but slightly smaller than too since we're approaching two from the left toe are approximation will give us I value very close to two. For the numerator and the denominator, its value smaller than to so about the smaller than to minus two, gives us a small negative number, especially when we are closest to the value. Two. This ratio of a finite number divided by a very small negative number. Give us a very large take a number. And so we can confirm that this limit tends towards negative infinity as X approaches to from the left for this function provided each of the steps. And we can confirm what the plot of the function, as you can see here centered around X equals two And is it Considine? When we approached two from the left, the function tends towards negative infinity, and this confirms our final answer.

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