A problem by Juliet Hanson

Level pending

lim ( sin 18x .cot6x) = ?

x--> 0

1 0 3 undetermined

Juliet Hanson by Juliet Hanson , 22, Iran

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2 solutions

we know that cotx=cosx/sinx. lim(sin18x . Cos6x/sin6x)= Multiply and devide by 18x Lim(18x . sin18x/18x) . lim (cos6x/sin6x) [bcoz.. limx→0 sinx/x=1] = lim( 18x . cos6x/ sin6x) =lim(3 . 6x . Cos6x/sin6x) = lim 3 . cos6x Lim x→0 =3 . 1 =3

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Juliet Hanson
Apr 16, 2015

We know that cot x =(tan x)^-1 & if x--> 0, then lim (tan x÷x)=1 & also if x--> 0, then lim(sin x÷x)=1 so lim (sin 18x.cotg6x) if x--> 0 =
lim(sin 18x÷tanx)=

X--> 0

lim [(sin 18x ×6x ×18x)÷(tan6x ×18x ×6x)]=

X--> 0

lim(18x÷6x)= lim 3 =3

X--> 0

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