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I know limits exist when we compute the limit from the right hand side and limit from the left hand side & they both equal but how can we find the limit by using only the limit laws? Is that possible?

Thank you.

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Computation of a limit ${\displaystyle \lim_{x\to a}}f(x)$ is entirely dependent on the function $f(x)$ and its properties. There is no catch-all method for quickly determining a limit. You must have some kind of understanding of how $f$ behaves on its domain. You come to this understanding from your knowledge of algebra, the real numbers, and functions on the real numbers. The limit laws follow from the properties of real numbers, but they're not of any use in actually computing the limit, aside from potentially simplifying the problem (e.g. factoring out constants, etc.).

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