find limit of x^2-1/x^2 - 2x + 1 as x approaches 1

Question

hartnn · Answer

can you factor numerator and denominator ?

hartnn · Answer

note that since we get 0/0 form
both numerator and denominator have (x-1) as their factor

anonymous · Answer

then i get x+1/x-1 , x cannot be = 1 still

hartnn · Answer

we need to consider left hand and right hand limits too
do you know what those are ?

anonymous · Answer

i got stuck there... Can you explain +infinity

hartnn · Answer

its not +infinity, sorry.
we need to consider left and right hand limits

anonymous · Answer

yeah i do knw about those...

hartnn · Answer

ok,
so can you find 
lim x->1$^-$ (x+1)/(x-1) 
?

hartnn · Answer

x->1$^-$ means x is very near to 1 but less than 1

hartnn · Answer

in that case x-1 will be negative
but very near to 0

hartnn · Answer

so the limit to x->1$^-$ will = - infinity

hartnn · Answer

but when x -> 1$^+$
x is very near to 1,but greater than 1
so,
x-1 will be very near to 0 , but positive.
so 
that limit = + infinity

hartnn · Answer

since these 2 limits are not equal,
the original limit 
x-> 1
will not exist.

anonymous · Answer

lol yeah de limit does not exist right?

hartnn · Answer

right.

anonymous · Answer

thnx hey

hartnn · Answer

welcome ^_^