Skip to main content\(\def\d{\displaystyle }
\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Worksheet Friday, 8/29
Let’s practice working with limits.
1.
Let
\(\d f(x) = \frac{x^2 + x - 2}{x^2 - 4}\text{.}\)
(a)
Find
\(\d\lim_{x \to 1}f(x)\text{.}\)
(b)
Find
\(\d\lim_{x \to 2}f(x)\text{.}\)
(c)
Find
\(\d\lim_{x \to -2}f(x)\text{.}\)
(d)
Find
\(\d\lim_{x \to 4}f(x)\text{.}\)
(e)
Find
\(\d\lim_{x \to \infty}f(x)\text{.}\)
2.
Evaluate the limit:
\begin{equation*}
\lim_{h \to 0} \frac{(2+h)^2 + 5(2+h) - (2^2 + 5\cdot 2)}{h}\text{.}
\end{equation*}
3.
Evaluate the limit:
\begin{equation*}
\lim_{a \to 4}\frac{\sqrt{a} - \sqrt{4}}{a - 4}
\end{equation*}
4.
For each of the two problems above, for what distance function does the limit represent an instantaneous velocity?
