what is the exact definition of limit?

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what is the exact definition of limit?

Precalculus
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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a limit is the value that a function or sequence "approaches" as the input or index approaches some value
delta epsilon defination of limit?
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Definition: \[\lim_{x \rightarrow a}f(x) = L\]means: for every epsilon > 0 there is a delta > 0 so that: if 0 < |x - a| < delta then |f(x) - L| < epsilon You have to learn this by heart! After that it takes some time and practice to understand what it means... It says in precise mathematical language: the nearer you choose your x-value to a, the nearer f(x) will be to L.

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