Indeterminate Forms

If the limits of f(x) and g(x) are equal to 0, as x tends to a, then f(x)/ g(x) is said to assume indeterminate form 0/0.
Some other indeterminate forms are ∞/∞, ∞ - ∞, 0×∞, 00, 1∞ and ∞0.

L’ Höpital’s rule
If  f(x) and g(x) are differentiable, g'(x) is not equal to zero for all x in the interval (a – h, a + h), except possibly at x = a, limits of f(x) and g(x) are equal to zero when x tends to a and limit of f'(x) / g' (x) exists finitely or infinitely when x tends to a,  then the limit of f(x)/ g(x) when x tends to a is equal to the limit of f'(x) / g' (x) when x tends to a.
L’ Höpital’s rule remains valid when the limit of f(x) as x tends to a is replaced by one sided limits.
L’ Höpital’s rule remains valid when the limits tend to negative infinity.
 

Keywords: L’ Höpital’s rule, Indeterminate forms

 

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