Question

2/ (x(x+2)). As lim of x approaches 0 ^- ,0^+ , and 0

Answer 1

Is it -infinity ,+infinity and ,doesnt exist respectively ?

Answer 2

\[\lim_{x \rightarrow 0} \frac{2}{x(x+2)} => \lim_{x \rightarrow 0} \frac{2}{x^2+2x} => \lim_{x \rightarrow 0} \frac{2/x^2}{x^2/x^2+2x/x^2}\]
\[\lim_{x \rightarrow 0} \frac{2/x^2}{1+2/x} =0\]

Answer 3

I mean = infinity

Answer 4

not 0 lol

Answer 5

Ah

Answer 6

limit doesnt exist because the left hand limit does not equal the right hand limit.

Answer 7

But what if x approaches 0 minus

Answer 8

negative infinity.

Answer 9

Now it makes sense, thanks

Answer 10

No problem.