Evaluate the following limit:
lim x -> 1 sin (x-1)/ (x^2 + x -2)
i got 1/3

- anonymous

Evaluate the following limit:
lim x -> 1 sin (x-1)/ (x^2 + x -2)
i got 1/3

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- anonymous

Did you use l'Hopital?

- anonymous

we didnt learn it yet so we cant use it

- anonymous

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

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## More answers

- myininaya

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

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

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

- anonymous

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

- anonymous

oh yay myiniaya! we did the same thing

- myininaya

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

- anonymous

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

- myininaya

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

- anonymous

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

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

- anonymous

the lim is x-> 1 though

- anonymous

I know it is.

- anonymous

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

- myininaya

what

- anonymous

lol so i cant use the squeeze theorem

- anonymous

what? You have to use squeeze theorem.

- myininaya

lol what polpak what are you saying to me

- myininaya

do you guys want me to prove it or not?

- anonymous

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

- myininaya

ok

- anonymous

then isnt my answer right

- anonymous

it is right.

- myininaya

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

- anonymous

i am a girl thank you very much

- anonymous

so whats the problem?

- anonymous

'he' is not gender specific.

- myininaya

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

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

- myininaya

oh lol sorry

- anonymous

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

- myininaya

no i don't believe you polpak

- anonymous

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

- anonymous

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

- myininaya

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

- anonymous

but purple is girly anyway were here for the math lol

- anonymous

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

- anonymous

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

- myininaya

no im here to defend my sex

- myininaya

lol

- anonymous

no i mean why is sinx/x = 1

- anonymous

no i mean why is sinx/x = 1

- myininaya

i will make you a proof k

- anonymous

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

- anonymous

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

- anonymous

It gets laggy when the question gets too long.

- anonymous

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

- anonymous

Of course.

- myininaya

##### 1 Attachment

- myininaya

i made you a pretty proof
its posted in the attachment

- anonymous

i'll post it somewhere else to cut the lag

- anonymous

aww :$ thank you

- myininaya

does it make sense alittle?

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