Now, it is the case that IF and ONLY IF the expression is both defined and continuous at the limiting value, then the limit can be found just by plugging in the limiting value. So, as you get closer and closer to x=0, clearly this is heading toward infinity.
You would not plug in x = 0, you would examine what happens when you get extremely close to x=0. The whole point in bothering with limits is finding ways of getting values that you cannot directly compute (usually division by 0 or other undefined or indeterminate forms). The limit is what you would be approaching as you got extremely close to, but not equal to, the limiting value. A limit is NOT what you would get if you actually did the math of the expression at the limiting value. This is an excellent question because it is a point that beginners are often confused about.
