# How do you find the limit of #sqrt(x-4)/(x-16)# as x approaches 16?

Yielding:

The problem then becomes:

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To find the limit of sqrt(x-4)/(x-16) as x approaches 16, we can use algebraic manipulation and the concept of limits. By factoring the denominator as (x-16), we can cancel out the common factor of (x-16) in both the numerator and denominator. This simplifies the expression to sqrt(x-4)/1, which is equivalent to sqrt(x-4).

Now, as x approaches 16, the expression sqrt(x-4) approaches sqrt(16-4) = sqrt(12) = 2√3. Therefore, the limit of sqrt(x-4)/(x-16) as x approaches 16 is 2√3.

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