IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

gaurav91

plz explain L HOSPITAL RULE

srujana

$If\;c\;is\;any\;finite\;number\; or\;\infty,$

$If\;\mathop{\lim}\limits_{{x} \to {c}}f(x)=0\;and\;\mathop{\lim}\limits_{{x} \to {c}}g(x)=0$

$then,\ \mathop{\lim}\limits_{{x} \to {c}}\frac{g(x)}{f(x)}=\mathop{\lim}\limits_{{x} \to {c}}\frac{g'(x)}{f'(x)}$

$If\;\mathop{\lim}\limits_{{x} \to {c}}f(x)=\infty\;and\;\mathop{\lim}\limits_{{x} \to {c}}g(x)=\infty$

$then,\ \mathop{\lim}\limits_{{x} \to {c}}\frac{g(x)}{f(x)}=\mathop{\lim}\limits_{{x} \to {c}}\frac{g'(x)}{f'(x)}$