help!
Find the limit ,use L'Hospital's Rule to solve.limx appropriate t,(1-sinx)/cscx. How to solve?

Question

help!
Find the limit ,use L'Hospital's Rule to solve.limx appropriate t,(1-sinx)/cscx. How to solve?

anonymous · Answer

remember. 1/cscx = sinx
and then the limit of a product is the product of the limits

anonymous · Answer

yeah,I know the form about this is 0/1,and I got the directive about this ,but what's the next steps?

dumbcow · Answer

what is x approaching in the limit ?

anonymous · Answer

infinity

anonymous · Answer

try convert it into $$\lim_{x \rightarrow \infty} (1-sinx) * \lim_{x \rightarrow \infty} (sinx) $$ to begin with

and then kick the constant (1) out the front of the limit

$$(1 - \lim_{x \rightarrow \infty} (sinx)) * (\lim_{x \rightarrow \infty} (sinx) )$$

and theeen - does those first steps help?

anonymous · Answer

yes!

dumbcow · Answer

but sin(infinity) is indeterminate ?

anonymous · Answer

right

anonymous · Answer

Yes u need to either change the limit or try by rationalizing the numerator

anonymous · Answer

try other method, take derivative of numerator & denominator first

anonymous · Answer

I don't know how to retionalizing the numerator,get the form to 0/0,or infin/infin

anonymous · Answer

to be honest i dont know if you can use l'hopitals with this one?

anonymous · Answer

maybe it can't use l'hospitals

anonymous · Answer

You cant use L'hopital.

anonymous · Answer

It has to be 0/0 or infinity/infinity. No exceptions.

anonymous · Answer

thanks,maybe it can't

anonymous · Answer

sinx values oscilate between -1 and 1 and therefor you don't/can't have an indeterminate form of infinity/infinity or 0/0 in the first place with this one

anonymous · Answer

^ What he said.

anonymous · Answer

yeah,I think so..

anonymous · Answer

Let x=(1/y) as y-->0 then x-->infinity 
Try using above substitutions. Although it still is a tough nut to crack :)

anonymous · Answer

who?

dumbcow · Answer

my answer would be as x->infinity the function oscillates between -2 and 1/4

anonymous · Answer

would you give me your steps? I want see you how to solve it

anonymous · Answer

Are you sure denominator is cosec x ?

anonymous · Answer

cscx,I am sure

anonymous · Answer

This should help .Its a output of a limit calculator

anonymous · Answer

attachment

anonymous · Answer

yes, so great!thank you very much

anonymous · Answer

L'Hopital's will definitely not work here, and you'll notice this will just oscillate without any clear limit.

anonymous · Answer

@Rachelzhang Anytime :)