- Asked 2/16
- 2074 Chaitra · 1 mark
- 2073 Chaitra
State L'Hospital's rule
Short answer
L'Hospital's rule: if lim f(x)/g(x) is an indeterminate form 0/0 or ∞/∞, then lim f(x)/g(x) = lim f'(x)/g'(x) provided the latter limit exists. The rule can be applied repeatedly, and other indeterminate forms must be converted to 0/0 or ∞/∞ first.
State L'Hospital's rule.
L'Hospital's rule. Let f and g be differentiable near a (except possibly at a), with g′(x) ≠ 0 near a. If lim_{x→a} f(x)/g(x) is of the indeterminate form 0/0 (or ∞/∞), then
lim_{x→a} f(x)/g(x) = lim_{x→a} f′(x)/g′(x),
provided the limit on the right exists (finite or infinite). The rule can be applied repeatedly if the form 0/0 or ∞/∞ persists.
Other forms (0·∞, ∞−∞, 1^∞, 0⁰, ∞⁰) are first converted to 0/0 or ∞/∞, using logarithms for the exponential forms.
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