# How do you find the limit of #(2x-8)/(sqrt(x) -2)# as x approaches 4?

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As an addition to the other answer, this problem can be solved by applying algebraic manipulation to the expression.

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To find the limit of (2x-8)/(sqrt(x) -2) as x approaches 4, we can use algebraic manipulation. First, we simplify the expression by multiplying both the numerator and denominator by the conjugate of the denominator, which is sqrt(x) + 2. This gives us (2x-8)(sqrt(x) + 2) in the numerator and (sqrt(x) -2)(sqrt(x) + 2) in the denominator. Simplifying further, we get (2x-8)(sqrt(x) + 2)/(x - 4). Now, we can substitute x = 4 into the expression, which gives us (2(4)-8)(sqrt(4) + 2)/(4 - 4). Simplifying this, we have (0)(4 + 2)/(0), which equals 0. Therefore, the limit of (2x-8)/(sqrt(x) -2) as x approaches 4 is 0.

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