Question

State L' Hospital's Rule

Answer 1

Answer:

L'Hôpital's rule states that, when the limit of f(x)/g(x) is indeterminate, under certain conditions it can be obtained by evaluating the limit of the quotient of the derivatives of f and g (i.e., f′(x)/g′(x)). If this result is indeterminate, the procedure can be repeated.

Step-by-step explanation:

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Answer 2

L' Hospital Rule :-

l' Hospital or l' Hopital Law states for any Limit of the form ;

$\quad \qquad { \bigstar { \underline { \boxed { \bf { \red { \displaystyle { \lim_{ \bf x \to c } \bf \dfrac{f ( x )}{g ( x )} }}}}}}}{\bigstar}$

If the Limit is $\tt \dfrac{0}{0}$ or $\tt \dfrac{\infty}{\infty}$ i.e Indeterminate form . The limit can be evaluated by Using l' Hopital Rule which is mathematically Represented as follows for the above limit !

$\quad \qquad { \bigstar { \underline { \boxed { \bf { \red { \displaystyle { \lim_{ \bf x \to c } \bf \dfrac{f' ( x )}{g'( x )} }}}}}}}{\bigstar}$

Where , f'(x) & g'(x) represents the Derivatives of the functions f(x) & g(x) respectively .

Or we can also say that ;

$\quad \qquad { \bigstar { \underline { \boxed { \bf { \red { \displaystyle { \lim_{ \bf x \to c } \bf \dfrac{f' ( x )}{g'( x )} = { \displaystyle { \lim_{ \bf x \to c } \bf \dfrac{f ( x )}{g ( x )}}} }}}}}}}{\bigstar}$

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