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