Evaluate the Limit

Problem

(lim_x→1)(√(,x−1)/(x−1))

Solution

1. Identify the form of the limit by substituting x=1 into the expression.

2. Observe that the expression results in the indeterminate form 0/0

3. Rewrite the denominator x−1 as (√(,x−1))2 for x>1 to facilitate cancellation.

4. Simplify the fraction by dividing the numerator and the denominator by √(,x−1)

√(,x−1)/((√(,x−1))2)=1/√(,x−1)

5. Evaluate the limit as x approaches 1 from the right, noting that the square root is undefined for x<1

(lim_x→1)(1/√(,x−1))=∞

Final Answer

(lim_x→1)(√(,x−1)/(x−1))=∞

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