Let f(x) = x^2 − 10x. If you construct an ϵ-δ proof to show that limx→5 f(x) = −25, what is the largest δ that would work for a given ϵ.

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A: I have explained everything with in the solution. Please go through that.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.