Question

How to evaluate limx→0(1/x−1/x²)?

Answer 1

To evaluate the limit limx→0(1/x−1/x²), simplify the expression step by step and substitute x = 0 into the simplified expression to find that the limit is undefined.

Step-by-step explanation:

To evaluate the limit limx→0(1/x−1/x²), we can simplify the expression step by step:

1. Combine the fractions in the numerator: (1/x) - (1/x²) = (x² - x)/x².
2. Simplify further: (x² - x)/x² = x(x - 1)/x² = (x - 1)/x.
3. Now, we can evaluate the limit as x approaches 0 by substituting x = 0 into the simplified expression: limx→0((x - 1)/x) = (0 - 1)/0 = -1/0, which is undefined.