Notes For Calculus Life Saver

3.2 the Left Side Limit and the Right Side Limit

Please think about what happens to h(x) when x is really close to 3.

If we get to the point of (3,1) from the left, we will get to the height of 1. But if we get to the point from the right, we will finally get to the height of -2. So we define that what approaches from the left the left side limit and what approaches from the right the right side limit. We write the left side limit like:

, and we write the right hand limit like . In this case,

and

And if the left side limit equals the right side limit, and the limit from both sides equals that number. If we write in the language of math, we’ll get: l=> .

But in this case, the left side limit doesn’t equal the right side limit, so we say the both sides limit does not exist. Or we can write it as , the DNE here stands for Does Not Exist.