Evaluate the Limit limit as x approaches 1 of 1/x

Problem

(lim_x→1)(1/x)

Solution

1. Identify the type of function. The function ƒ(x)=1/x is a rational function.

2. Check for continuity at the target value. A rational function is continuous at all points in its domain, which includes all x≠0

3. Apply the direct substitution property. Since x=1 is in the domain of the function, the limit is equal to the function value at that point.

4. Substitute x=1 into the expression.

1/1=1

Final Answer

(lim_x→1)(1/x)=1

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