Subjects calculus

Limit At Zero A835Fc

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Limit At Zero A835Fc


1. The problem asks: What is the limit of the function as $x$ approaches 0 based on the given graph description? 2. From the description, the function has a vertical asymptote at $x=0$, where the $y$ values diverge towards positive or negative infinity. 3. Recall that if a function approaches infinity or negative infinity near a point, the limit does not exist in the finite sense but can be described as infinite. 4. Since the graph goes down steeply from $y=10$ near $x=0$ from the left side and diverges, and the function values diverge towards infinity or negative infinity at $x=0$, the limit does not exist finitely. 5. Therefore, the limit of the function as $x$ approaches 0 is: $$\lim_{x \to 0} f(x) = \pm \infty$$ meaning the function diverges to infinity or negative infinity and the limit does not exist in the finite sense. This completes the solution for the first question.