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Finding the limit of a function involving a square root can be challenging. However, there are specific techniques that can be employed to simplify the process and obtain the correct result. One common method is to rationalize the denominator, which involves multiplying both the numerator and the denominator by a suitable expression to eliminate the square root in the denominator. This technique is particularly useful when the expression under the square root is a binomial, such as (a+b)^n. By rationalizing the denominator, the expression can be simplified and the limit can be evaluated more easily.

For example, consider the function f(x) = (x-1) / sqrt(x-2). To find the limit of this function as x approaches 2, we can rationalize the denominator by multiplying both the numerator and the denominator by sqrt(x-2):

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In mathematics, a limit is the value that a function approaches as the input approaches some value. Limits are used to define derivatives, integrals, and other important mathematical concepts. When the input approaches infinity, the limit is called an infinite limit. When the input approaches a specific value, the limit is called a finite limit.

Finding the limit of a function can be challenging, especially when the function involves roots. However, there are a few general techniques that can be used to find the limit of a function with a root.

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