Evaluate the following limit:

lim x - 1 sin (x-1)/ (x^2 + x -2)

i got 1/3

Question

Evaluate the following limit:

lim x -> 1 sin (x-1)/ (x^2 + x -2)

i got 1/3

anonymous · Answer

Did you use l'Hopital?

anonymous · Answer

we didnt learn it yet so we cant use it

anonymous · Answer

I think you have to. You have 0 over 0 here.

myininaya · Answer

sin(x-1)/(x-1)(x+2)
sin(x-1)/(x-1)->1 as x->1
so now we have 1/(x+2)->1/3 since x->1

anonymous · Answer

this is what i did

lim x-> 1 sin (x-1)/(x-1)(x+2)
               sin (x-1)/x-1 x 1/x+2
               then substitute the lim in
1x 1/3
1/3

myininaya · Answer

remember sinx/x->1 as x->0
so sin(x-1)/(x-1)->1 as x->1

anonymous · Answer

sin(x-1)/(x-1)->1 as x->1 using l'Hopital?

anonymous · Answer

oh yay myiniaya! we did the same thing

myininaya · Answer

no using sinx/x->1 as x->0

anonymous · Answer

yes, but how do you evaluate that limit without l'hopital?

myininaya · Answer

we could use the squeeze theorem to show sinx/x->1 as x->0

anonymous · Answer

I mean someone could tell you, but they would have had to do it. Or I guess squeeze theorem. But either way I'd like to see more of a justification there.

myininaya · Answer

i could totally prove this sinx/x thing give me a sec and i will post

anonymous · Answer

the lim is x-> 1 though

anonymous · Answer

I know it is.

anonymous · Answer

I just don't know that you know it is ;p

myininaya · Answer

what

anonymous · Answer

lol so i cant use the squeeze theorem

anonymous · Answer

what? You have to use squeeze theorem.

myininaya · Answer

lol what polpak what are you saying to me

myininaya · Answer

do you guys want me to prove it or not?

anonymous · Answer

no. I'm good. I was just saying that purp should give some justification when he uses it in his argument

myininaya · Answer

ok

anonymous · Answer

then isnt my answer right

anonymous · Answer

it is right.

myininaya · Answer

yes it is 
i think polpak just wants you to understand why sinx/x->1 as x->0

anonymous · Answer

i am a girl thank you very much

anonymous · Answer

so whats the problem?

anonymous · Answer

'he' is not gender specific.

myininaya · Answer

im a girl too.
what do you mean you are a girl?
are you saying we can't do math as well as guys?

anonymous · Answer

she means I said 'he' before and she was correcting my use of that pronoun

myininaya · Answer

oh lol sorry

anonymous · Answer

but 'he' is correct usage when you don't know the person's gender.

myininaya · Answer

no i don't believe you polpak

anonymous · Answer

why? exactly is that because my teacher did this long proof on the board

anonymous · Answer

it's true! she is gender specific. he is not.

myininaya · Answer

don't  make me growl
i do not want to be referred to as a he

anonymous · Answer

but purple is girly anyway were here for the math lol

anonymous · Answer

Well now that I know you are a woman I will refer to you as she if it makes you feel better =)

anonymous · Answer

http://en.wikipedia.org/wiki/Gender-neutral_pronoun

myininaya · Answer

no im here to defend my sex

myininaya · Answer

lol

anonymous · Answer

no i mean why is sinx/x = 1

anonymous · Answer

no i mean why is sinx/x = 1

myininaya · Answer

i will make you a proof k

anonymous · Answer

because it is. You can prove that it is using the sqeeze theorem or l'hopitals.

anonymous · Answer

this website is freezing please dont type fast we'll confuse ourselves

anonymous · Answer

It gets laggy when the question gets too long.

anonymous · Answer

ok thank you gents {i assume} will you help me with my other questions

anonymous · Answer

Of course.

myininaya · Answer

attachment

myininaya · Answer

i made you a pretty proof 
its posted in the attachment

anonymous · Answer

i'll post it somewhere else to cut the lag

anonymous · Answer

aww :$ thank you

myininaya · Answer

does it make sense alittle?