Skip to main content
Contents Index Dark Mode Prev Up Next Scratch ActiveCode Profile \(\newcommand{\dollar}{\$}
\DeclareMathOperator{\erf}{erf}
\DeclareMathOperator{\arctanh}{arctanh}
\DeclareMathOperator{\arcsec}{arcsec}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Activity 1.2.2 .
Estimate the value of each of the following limits by constructing appropriate tables of values. Then determine the exact value of the limit by using algebra to simplify the function. Finally, plot each function on an appropriate interval to check your result visually.
(a)
\(\displaystyle \lim_{x \to 1} \frac{x^2 - 1}{x-1}\)
(b)
\(\displaystyle \lim_{x \to 0} \frac{(2+x)^3 - 8}{x}\)
(c)
\(\displaystyle \lim_{x \to 0} \frac{\sqrt{x+1} - 1}{x}\)
