Question

How do you find the limit `(2+1/x)/(3-2/x)` as `x->0`?

Answer 1

Multiply by `x/x`, and then let `xto0`, to find that the limit is `-1/2`

Explanation:

Given: `lim_(xto0)(2 + 1/x)/(3 - 2/x)`

Multiply by 1 in the form of `x/x`:

`lim_(xto0)(2 + 1/x)/(3 - 2/x)x/x =`

`lim_(xto0)(2x + 1)/(3x - 2)`

Let `xto0`: `1/-2 = -1/2`