X times X -4 / X-2. let X=2=0 Now try X=1.9,1.99,1.999ect. As X tends towaards 2,answer tends towards 4. WHY??

Question

I'm not sure of the reason why.

Answer 1

You have (x^2 - 4) / (x-2)
But x^2 - 4 = (x+2) * (x-2)
So the x-2 in the num and denom cancels leaving
x+2
So 2+ 2 = 4

We say that (x^2 - 4) / (x-2) has a removable discontinuity at x = 2

Answer 2

One can refactor (x * x) - 4 into (x + 2)(x - 2). When this quantity is divided by (x - 2), the result should be (x + 2). As x -> 2, the quantity (x + 2) -> 4. Thus, 4 is also the limit of the quantity ((x * x) - 4 / x - 2) as x -> 2.

Answer 3

LIM AS x approaches 2 OF: (x^2-4)/(x-2) =
LIM AS x approaches 2 OF: (x+2)(x-2)/(x-2) =
LIM AS x approaches 2 OF: x+2 =
4

Answer 4

well i think that x is not equal to 2 though...... if x= 2 then that should give u undefined..... which means u probably got a left limit and a right limit, try it from the other side and see

Answer 5

This has to do with the consideration that you are dealing with the entire function. If you take its derivitive and evaluate, it should exist at x=2.

Answer 6

you can always use L'hospital's rules as well (if you've learned it)..

lim [(x^2-4)/(x-2)]
x->2

lim [(x^2-4)'/(x-2)']
x->2

lim [2x/1]
x->2

lim (2x) = 2*2 = 4
x->2

Answer 7

because