In Class Practice $1$

The problems below are meant to give some additional practice with topics we've worked on in class over the last few days.

Feel free to work with those around you and ask me any questions.

Turn in your solutions and work at the end of class $($make sure to put your name on it$!)$

Consider the limit: $\underset{x0}{lim}\frac{\sqrt[\phantom{2}]{x+1}-1}{x}$

$($a$)$ Explain clearly why direct substitution does not work for this limit$.$

$($b$)$ Fill out the following table of values for this function and estimate the limit:

$\backslash$table$[[x,-0\mathrm{.}1,-0\mathrm{.}01,-0\mathrm{.}001,0,0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}1],[f(x),,,,,,,]]$

$($c$)$ Use the rationalizing method to find the limit algebraically.

$2.$ The graph below shows the function $g(x).$ Evaluate the following limits$,$ or explain why they do not exist.

$($a$)\underset{x0}{lim}g(x)$

$($b$)\underset{x2}{lim}g(x)$

$($c$)\underset{x3}{lim}g(x)$

$3.$ Compute the following limits$,$ or explain why they do not exist:

$($a$)\underset{x0}{lim}(3x-2{)}^4$

$($b$)\underset{?}{lim}\frac{\sqrt[\phantom{2}]{x+6}}{n}$