Evaluate the Limit limit as x approaches 1 of |x-1|

Problem

(lim_x→1)(x−1)

Solution

1. Identify the type of function. The function ƒ(x)=|x−1| is an absolute value function, which is continuous everywhere on the real number line.

2. Apply the direct substitution property for limits of continuous functions. Since the function is continuous at x=1 the limit is equal to the function value at that point.

3. Substitute x=1 into the expression.

|1−1|

4. Simplify the result of the subtraction inside the absolute value.

|0|

5. Evaluate the absolute value of zero.

0

Final Answer

(lim_x→1)(x−1)=0

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