The lecture note covers the topic of finding limits of polynomial, rational, and radical functions. It starts by explaining how to find limits of polynomial functions by using properties of limits to break the polynomial into individual terms, finding the limits of each term, and adding them back together.
Next, it covers how to find limits of rational functions. The main methods discussed are factoring the numerator and denominator completely, simplifying by canceling common factors, and then evaluating the resulting limit. Another method is direct substitution as long as it does not result in dividing by zero.
Finally, the lecture note explains how to find limits of radical functions. It emphasizes first trying direct substitution if possible. If that doesn't work, it introduces using the conjugate of binomial radical expressions in order to evaluate limits involving them. Examples show step-by-step how to properly apply the conjugate method to simplify the limit expression and then evaluate the limit. Additional examples of evaluating limits of radical functions using direct substitution are also provided.
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