❤︎² Find a Limit Algebraically.. How? (mathbff)

There isn’t any one algebraic method that will works for finding every limit. Here are the different methods:

1) Direct Substitution (0:22)
When trying to evaluate a limit algebraically your “go to" method should be direct substitution. If direct substitution works, simply plug in the value that x is approaching, and evaluate the function.

2) What about if I get 0/0? (1:25)
If you try direct substitution and get 0/0 (the indeterminate form), you should try to simplify the function and then try direct substitution again.

3) Factor to Simplify (2:17)
If you see higher powered polynomials in the function, you should try a form of factoring to simplify the function. Whether it is a difference of squares or cubes, a perfect square trinomial, a trinomial with or, or even a grouping situation, factoring will usually get you to the result. Once you’ve simplified by factoring, try direct substitution again.

4) Use a Conjugate to Simplify (4:28)
If you see a root in the function, you should try multiplying by the conjugate of the root to simplify the function. Once the function is simplified, try direct substitution again.

5) Use Expansion of Polynomials to Simplify (7:09)
If you tried factoring and weren’t able to simplify, you can try expanding any polynomials which are raised to a power, then check for anything that cancels out. Once you’ve simplified by canceling out terms, try direct substitution again.

6) Simplify With a Common Denominator (8:38)
If you have a complex fraction, you can try using a common denominator to simplify the fractions. Once you’ve simplified the fractions, try direct substitution again.

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