Question

evaluate limit as x goes to 2 = sin(x-2)/(x^2-4)

Answer 1

infinity

Answer 2

take the limit of top and bottom sin(0) = 1

(2^2 - 4) aproaches 0 BUT can never go to zero because you cant divide by zero

Answer 3

so as the denominator goes to 0.00000001 or 0.000000000000000001

Answer 4

its ilike this 1/4 then 1/2 then 1/1 then 1/0.000001 then 1/0.0000000000001

Answer 5

This one can be handled with a little manipulation. The bottom can be expanded to (x-2)(x+2). The lim of [sin (x-2)]/(x-2)]=1. That leaves 1/(x+2). So lim is 1/4.

Answer 6

no the bottom cannot be expanded like that

Answer 7

I am guessing by the way these questions are set up that x^2-4 is not sin of, but just a number.

Answer 8

I think the its sin of x-2 so sin(x-2)

Answer 9

divided by x^2 - 4

Answer 10

In that case we are saying the same thing. \[x ^{2}-4=(x-2)(x+2)\]The difference of two squares.

Answer 11

no thats what you are saying

Answer 12

that is impossible to do

Answer 13

I have had a couple beers. But are you telling me that the above is not the difference of two squares?

Answer 14

no it is

Answer 15

maybe your right im sorry

Answer 16

limit as x goes to 2 = sin(x-2)/(x^2-4)
0/0 so Use L'Hopital's rule

lim x->2 Cos(x-2)/(2x) = Cos (0) / (2*2) = 1/4