L'Hôpital's Rule Quiz

L'Hôpital's rule is named after the 17th-century French mathematician Guillaume de l'Hôpital.

The theorem was first introduced to Guillaume de l'Hôpital in 1694 by the Swiss mathematician Johann Bernoulli.

The conditions for applying L'Hôpital's rule to functions f and g are: lim x → c f ( x ) = lim x → c g ( x ) = 0 or ± ∞, g ′ ( x ) ≠ 0 for all x in I with x ≠ c, and lim x → c f ′ ( x ) g ′ ( x ).

<p>L'Hôpital's rule states that if lim x → c f ( x ) = lim x → c g ( x ) = 0 or ± ∞, and g ′ ( x ) ≠ 0 for all x in I with x ≠ c, then lim x → c f ′ ( x ) g ′ ( x ).</p> Signup and view all the answers

<p>L'Hôpital's rule is also known as Bernoulli's rule.</p> Signup and view all the answers

<p>Number theory, algebra, geometry, and analysis.</p> Signup and view all the answers

<p>The discovery of properties of abstract objects and the use of pure reason to prove them.</p> Signup and view all the answers

<p>A succession of applications of deductive rules to already established results.</p> Signup and view all the answers

<p>Abstractions from nature or entities stipulated to have certain properties, called axioms.</p> Signup and view all the answers

<p>Previously proved theorems, axioms, and some basic properties considered true starting points of the theory.</p> Signup and view all the answers

<p>number theory, algebra, geometry, and analysis</p> Signup and view all the answers

<p>the discovery of properties of abstract objects and the use of pure reason to prove them</p> Signup and view all the answers

<p>abstractions from nature or entities stipulated to have certain properties, called axioms</p> Signup and view all the answers

<p>a succession of applications of deductive rules to already established results</p> Signup and view all the answers

<p>previously proved theorems, axioms, and some basic properties considered true starting points</p> Signup and view all the answers