Please Help Me Find the Limit?

Question

x-->2

x^2 - 4

----------

x^2 - 2x

Answer 1

You can factor,

(x-2)(x+2)/x(x-2)

(x-2)/x

4-2/4

2/4

1/2

Answer 2

factor the top and bottom...

[(x + 2)(x - 2)]/[x(x - 2)]

(x - 2)'s cancel, so

lim(x-->2) (x + 2)/x = (2 + 2)/2 = 2

2 is the limit

to monu and cidyah: given the time of year, and the level of difficulty of this limit, I highly doubt he is familiar with L'Hopital's rule. No need to show off

Answer 3

  lim     x^2 -4

  x->2   ---------

            x^2 - 2x

since when u put the limit u get 0/0 form so u have to use L' hospital's rule wherein u have to differentiate numerator and denominator separetely

so u get

   lim     2x

  x->2   ---------

            2x - 2

now putting the limit u get

  =4 / (4-2)

  =  4/2  =  2

Answer 4

L'Hopital's Rule

lim x->2 2x / 2x-2

lim x->2 2 / 2 = 4/2 =2

Without L'Hopital's Rule

(x+2)(x-2) / x(x-2) = (x+2)/x =

as x->2 this ratio tends to 2

Answer 5

simplify to get

x-->2

x+2

-----

x

then

2+2

-----

2

gives 4/2=2

Answer: 2