Definitions [1]
Definition: Indeterminate Forms
At x = a, if f(x) takes any of the forms \[\frac{0}{0}\], \[\frac{∞}{∞}\], 0 × ∞, 0°, 1∞. 0∞ and ∞0, then f(x) is said to be indeterminate at x = a.
Other indeterminate forms are first reduced to the forms \[\frac{0}{0}\], \[\frac{∞}{∞}\].
Theorems and Laws [1]
Rule: L’Hôpital’s rule
- \[\lim_{x\to a}f(x)=0\mathrm{~and}\lim_{x\to a}g(x)=0\mathrm{,or"}\]
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\[“\lim_{x\to a}f(x)=\infty\mathrm{~and}\lim_{x\to a}g(x)=\infty,\]
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both f(x) and g(x) are differentiable in a neighbourhood of x = a,
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g′(x) ≠ 0
then \[\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f^{\prime}(x)}{g^{\prime}(x)}\]
provided the limit on the right-hand side exists.
