Evaluate the Limit

Problem

(lim_x→16)((x−16)/(√(,x)−4))

Solution

1. Identify the indeterminate form by substituting x=16 into the expression, which results in 0/0

2. Factor the numerator using the difference of squares formula, a2−b2=(a−b)*(a+b) where x=(√(,x))2 and 16=4

3. Rewrite the expression with the factored numerator.

((√(,x)−4)*(√(,x)+4))/(√(,x)−4)

4. Simplify the expression by canceling the common factor (√(,x)−4) from the numerator and the denominator.

√(,x)+4

5. Evaluate the limit by substituting x=16 into the simplified expression.

√(,16)+4

6. Calculate the final numerical value.

4+4=8

Final Answer

(lim_x→16)((x−16)/(√(,x)−4))=8

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