$\rhd$ Limit properties (5:07) What is the limit of the sum of two functions? Difference? What about the product? Division? A function rasised to a number?
$\rhd$ Limits of combined functions (4:08) Given the graphs of $f(x)$ and $h(x)$, find $\displaystyle\lim_{x\to 0}(f(x)h(x))$. Then, given the graphs of $g(x)$ and $h(x)$, find $\displaystyle\lim_{x\to 0}\dfrac{h(x)}{g(x)}$.
$\rhd$ Limits of combined functions: piecewise functions (4:12) The graphs of two piecewise functions, $f(x)$ and $g(x)$, are given. Find $\displaystyle\lim_{x\to -2}(f(x)+g(x))$, $\displaystyle\lim_{x\to 1}(f(x)+g(x))$ and $\displaystyle\lim_{x\to 1}(f(x)g(x))$.
* Practice: Limits of combined functions: sums and differences. (4 problems)
* Practice: Limits of combined functions: products and quotients. (4 problems)
$\rhd$ Limits of composite functions (5:11) Given the graphs of $g(x)$ and $h(x)$, find $\displaystyle\lim_{x\to 3}(g(h(x))$. Then, given the graphs of other functions $g(x)$ and $h(x)$, find $\displaystyle\lim_{x\to -1}h(g(x))$. Two more graphs are given for the functions $h(x)$ and $f(x)$ to find $\displaystyle\lim_{x\to -3}h(f(x))$.
* Practice: Limits of composite functions. (4 problems)
Evaluating limits using algebraic manipulations
$\rhd$ Limits by factoring (5:44) Find $\displaystyle\lim_{x\to 2}\dfrac{x^2+x-6}{x-2}$.
