Hospital's Rate
Suppose t andg are differentiable and g coal 0
on an open interval I containing a except possibly at a
Eimate Simas out ama
m
gX
IRI Not obvious
Also holds for a at 1a fool
Examples Conditions are met
Siu x l XcxLim Lim T cos co Ix O K K 30
Luca 1Lim Lim Lim E Ox of 11 K 30 22C a
tubal jLim seen x Lim LimOt o Ise o
2
Limx ot
X o
Mmegenerally i Indeterminautform
feime.tt o Is 9 in tc goal
7 x7 Gygax C Apply L'Hospital
Ight
ly Lim e aK a Indeterminant Form
Lim e a Lim x a Lim e ax a x x
Lim ex x Lima
K ea
x
piedTc
Lim ekLim T aK a
feisal ilLim x
a
move generally Indeterminant Form
iz 7 0
is 9cal I ing ten goal
Convert to Product gCx tg and calculate1 Gyim using L Hospital If product is indeterminantx
ie Luiz tg I apply indeterminat product method
Lim x 2a Ot Recall a elute
exponentials are Ctsim x Lim ext Felkins alumx 3 Ot a
5013Lim setula O Liar x Ia Otx Ot
More generallyIn determinant
Formim 7cal O Ling guy oc 7
im 7cal faith guy o Lion CHPx 7 X
im 7cal I Ling guy Ax
ten 944 es tgig tea 9 e.ITgcMlucHxD
gCalculate usingin determinantproduct method