limits question (1 Viewer)

[tacogym27101990]

hey sorry to bother yall
but im doing some papers for my dif cal exam next week
and i ran into one i had trouble with:
lim(y>0+) (cosh(3/y))^y

this is my work so far:
let L be the limit it approaches
so lnL=lim(y>0+) ycosh(3/y)
=lim(y>0+)(cosh(3/y))/y^-1 which is in the form (inf/inf)

so using l'hopitals:
=lim(y>0+) 3sinh(3/y)
=inf
so L=e^inf
=inf

but the answers say 3
any help would be appreciated, thanks

 

[shaon0]

hey sorry to bother yall
but im doing some papers for my dif cal exam next week
and i ran into one i had trouble with:
lim(y>0+) (cosh(3/y))^y

this is my work so far:
let L be the limit it approaches
so lnL=lim(y>0+) ycosh(3/y)
=lim(y>0+)(cosh(3/y))/y^-1 which is in the form (inf/inf)

so using l'hopitals:
=lim(y>0+) 3sinh(3/y)
=inf
so L=e^inf
=inf

but the answers say 3
any help would be appreciated, thanks

Is the answer: e^3 ?

 

[lolokay]

hey sorry to bother yall
but im doing some papers for my dif cal exam next week
and i ran into one i had trouble with:
lim(y>0+) (cosh(3/y))^y

this is my work so far:
let L be the limit it approaches
so lnL=lim(y>0+) ycosh(3/y)
=lim(y>0+)(cosh(3/y))/y^-1 which is in the form (inf/inf)

so using l'hopitals:
=lim(y>0+) 3sinh(3/y)
=inf
so L=e^inf
=inf

but the answers say 3
any help would be appreciated, thanks

should this be lnL=lim(y>0+) yln[cosh(3/y)] ?

 

[tacogym27101990]

should this be lnL=lim(y>0+) yln[cosh(3/y)] ?

argh thanks i hate stupid mistakes!!