Question

lim x→-2 x+2/√(x^2-4)

Answer 1

I'm not sure if there is a simpler way to do this or not.

Since both the top and the bottom approach 0 as x goes to -2, we can use L'Hopital's rule. This means that we take the derivative of the top and divide it by the derivative of the bottom to get the limit.

lim x→-2 1/((1/2)(x^2)^-1/2)(2x) = lim x→-2 1/((1/2)(x^2)^(-1/2))(2x)

Plugging in -2 we get 1/((1/2)(1/2)(-4) = 1/-1 = -1.

Hopefully this helps, sorry about the hideous formatting.