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Use the graph of the function $ f $ to state the value of each limit, if it exists. If it does not exist, explain why.

(a) $ \displaystyle \lim_{x \to 0^-}f(x) $

(b) $ \displaystyle \lim_{x \to 0^+}f(x) $

(c) $ \displaystyle \lim_{x \to 0}f(x) $

$ \displaystyle f(x) = \frac{x^2 + x}{\sqrt{x^3 + x^2}} $

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Missouri State University

Oregon State University

Harvey Mudd College

Mrs Problem number fourteen Stuart, eighth edition, section two point two He's the graph of the function F to state the value of each limit. If it exists, it is not explain why. So we take a look at their plot using neither crapping calculator Ah, this Excel spreadsheet or any other graphing the tool. And we take this function and plot it and we're gonna be planting around X equals zero because that is the location of interest. And to answer party the limit of this as experts zero from the left, we see that the behavior you Raph approaching through from the left is equal to negative one. And that is the left hand limit. Take a look at the graph again, per p. The limit of F as experts zero from the right. We follow the behavior of the function and we see that it approaches approximately one positive one as we traced the function from the right zero towards zero. Finally, the limit as expert is zero of the function AF has to do with both the left hand lemon and the right hand woman. They both exist, but they are not in agreement. Make it one on one are different parts of the graph and therefore we say that the limit had, as experts zero in totality does not exist.