Example 3

If ε ≠ 0, the quotient

is finite but not infinitesimal.

Cancelling an ε from numerator and denominator, we get

(2)

Since 3ε² + ε. is infinitesimal while -6 is finite but not infinitesimal, the numerator

3ε² + ε - 6

is finite but not infinitesimal. Similarly, the denominator 2ε + 1, and hence the quotient (2) is finite but not infinitesimal.