Evaluate the Limit limit as x approaches 0 of (x^2-x)/x

Problem

(lim_x→0)((x2−x)/x)

Solution

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

2. Factor the numerator by taking out the greatest common factor, which is x

(x*(x−1))/x

3. Simplify the expression by canceling the common factor x from the numerator and the denominator, noting that x≠0 as it approaches the limit.

x−1

4. Evaluate the limit by substituting x=0 into the simplified expression.

0−1=−1

Final Answer

(lim_x→0)((x2−x)/x)=−1

Want more problems? Check here!