[math] \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow} \newcommand{\ddxof}[1]{\frac{d #1}{d x}} \newcommand{\ddx}{\frac{d}{dx}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\dydx}{\ddxof y} \newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}} \newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}} \newcommand{\dist}{\mathrm{distance}} \newcommand{\arccot}{\mathrm{arccot\:}} \newcommand{\arccsc}{\mathrm{arccsc\:}} \newcommand{\arcsec}{\mathrm{arcsec\:}} \newcommand{\arctanh}{\mathrm{arctanh\:}} \newcommand{\arcsinh}{\mathrm{arcsinh\:}} \newcommand{\arccosh}{\mathrm{arccosh\:}} \newcommand{\sech}{\mathrm{sech\:}} \newcommand{\csch}{\mathrm{csch\:}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\mathds}{\mathbb} [/math]

Compute the following limits.

• [math]\lim_{x \goesto 1} \frac{x^3-1}{x-1}[/math]
• [math]\lim_{x \goesto 2} \frac{x^2 - 5x +6}{x-2}[/math]
• [math]\lim_{x \goesto 3} \frac{x^2-5x+6}{x-3}[/math]
• [math]\lim_{x \goesto 1} \left( \frac{x^2}{x-1} - \frac{1}{x-1} \right)[/math]
• [math]\lim_{x \goesto 0} x^{\frac32}[/math]
• [math]\lim_{x \goesto 0} \frac{\sqrt{x+1}-1}x[/math]
• [math]\lim_{x \goesto 0} |x|[/math]
• [math]\lim_{h \goesto 0} \left( \frac{1-h^2}{h^2} + \frac{6h^2-1}{h^2} \right )[/math]
• [math]\lim_{x \goesto 0} \frac{(a+x)^3 + 2(a+x) - a^3 - 2a}x[/math]
• [math]\lim_{h \goesto 0} \frac{2(x+h)^2 - (x+h) - 2x^2 +x}h[/math].