Question

Evaluate the following limit:

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

i got 1/3

Answer 1

Did you use l'Hopital?

Answer 2

we didnt learn it yet so we cant use it

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

oh yay myiniaya! we did the same thing

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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.

Answer 13

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

Answer 14

the lim is x-> 1 though

Answer 15

I know it is.

Answer 16

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

Answer 17

what

Answer 18

lol so i cant use the squeeze theorem

Answer 19

what? You have to use squeeze theorem.

Answer 20

lol what polpak what are you saying to me

Answer 21

do you guys want me to prove it or not?

Answer 22

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

Answer 23

ok

Answer 24

then isnt my answer right

Answer 25

it is right.

Answer 26

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

Answer 27

i am a girl thank you very much

Answer 28

so whats the problem?

Answer 29

'he' is not gender specific.

Answer 30

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

Answer 31

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

Answer 32

oh lol sorry

Answer 33

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

Answer 34

no i don't believe you polpak

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

but purple is girly anyway were here for the math lol

Answer 39

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

Answer 40

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

Answer 41

no im here to defend my sex

Answer 42

lol

Answer 43

no i mean why is sinx/x = 1

Answer 44

no i mean why is sinx/x = 1

Answer 45

i will make you a proof k

Answer 46

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

Answer 47

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

Answer 48

It gets laggy when the question gets too long.

Answer 49

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

Answer 50

Of course.

Answer 51

i made you a pretty proof
its posted in the attachment

Answer 52

i'll post it somewhere else to cut the lag

Answer 53

aww :$ thank you

Answer 54

does it make sense alittle?