Limits

A limit is a method to get a calculation value indirectly when a division by zero error prevents a direct calculation.

To provide most of the idea, we start with a very simple problem that we could calculate:

What is x+3 approaching as x approaches 2?

Even though you probably haven’t seen this type of problem for, I’m guessing you will, after a few seconds, say, x + 3 is approaching five.

That is correct. We will show this with notation below:

Limit

\displaystyle \lim_{x\to2}x+3=5

Limits of Monomials

  • If n is positive, \displaystyle \lim_{x \to 0} x^n = 0
  • If n=0, \displaystyle \lim_{x \to 0} x^0 = 1
  • If n is negative, \displaystyle \lim_{x \to 0} x^n = indeterminant

regarding the last one, let m=-n and then x^n = \dfrac {1}{x^m}

Ignore content below

We are testing latex co

Summation

\displaystyle \sum_{n=1}^{\infty} \dfrac{1}{n}=2

Integration

\displaystyle\int_{t_{i}}^{t_{f}}a dt=|_{a}^{b}