Evaluate the Limit

Problem

(lim_x→100)((√(,x)−10)/(x−100))

Solution

1. Identify the indeterminate form by substituting x=100 into the expression, which results in 0/0

2. Rationalize the numerator by multiplying both the numerator and the denominator by the conjugate of the numerator, which is √(,x)+10

3. Simplify the numerator using the difference of squares formula, (a−b)*(a+b)=a2−b2 which gives (√(,x))2−10=x−100

4. Cancel the common factor of x−100 from both the numerator and the denominator.

5. Evaluate the limit by substituting x=100 into the remaining expression.

Final Answer

(lim_x→100)((√(,x)−10)/(x−100))=1/20

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