Resolución de Límites Trigonométricos II

$f left parenthesis x right parenthesis equals fraction numerator sin open parentheses x close parentheses cubed over denominator open parentheses 2 x close parentheses cubed end fraction space semicolon fraction numerator s i n open parentheses x close parentheses cubed over denominator x cubed end fraction equals open parentheses fraction numerator s i n open parentheses x close parentheses over denominator x end fraction close parentheses cubed stack l i m with x rightwards arrow 0 below space space fraction numerator s i n open parentheses x close parentheses cubed over denominator open parentheses 2 x close parentheses cubed end fraction equals stack l i m with x rightwards arrow 0 below space space fraction numerator s i n open parentheses x close parentheses cubed over denominator 8 x cubed end fraction equals 1 over 8 stack l i m with x rightwards arrow 0 below space space fraction numerator s i n open parentheses x close parentheses cubed over denominator x cubed end fraction equals 1 over 8 space stack l i m with x rightwards arrow 0 below space space fraction numerator s i n open parentheses x close parentheses cubed over denominator x cubed end fraction equals 1 over 8 space stack l i m with x rightwards arrow 0 below space space open parentheses fraction numerator s i n open parentheses x close parentheses over denominator x end fraction close parentheses cubed equals 1 over 8 open parentheses 1 close parentheses cubed stack l i m with x rightwards arrow 0 below space space fraction numerator s i n open parentheses x close parentheses cubed over denominator open parentheses 2 x close parentheses cubed end fraction equals 1 over 8$

$g left parenthesis x right parenthesis equals fraction numerator tan open parentheses 3 x close parentheses over denominator x end fraction stack l i m with x rightwards arrow 0 below space fraction numerator t a n open parentheses 3 x close parentheses over denominator x end fraction equals stack l i m with x rightwards arrow 0 below space fraction numerator begin display style fraction numerator sin open parentheses 3 x close parentheses over denominator cos open parentheses 3 x close parentheses end fraction end style over denominator x end fraction equals stack l i m with x rightwards arrow 0 below space fraction numerator s i n open parentheses 3 x close parentheses over denominator x c o s open parentheses 3 x close parentheses end fraction equals stack l i m with x rightwards arrow 0 below space fraction numerator s i n open parentheses 3 x close parentheses over denominator x end fraction fraction numerator 1 over denominator c o s open parentheses 3 x close parentheses end fraction equals stack l i m with x rightwards arrow 0 below space 3 fraction numerator s i n open parentheses 3 x close parentheses over denominator 3 x end fraction fraction numerator 1 over denominator c o s open parentheses 3 x close parentheses end fraction stack l i m with x rightwards arrow 0 below space fraction numerator t a n open parentheses 3 x close parentheses over denominator x end fraction equals stack l i m with x rightwards arrow 0 below space 3 fraction numerator s i n open parentheses 3 x close parentheses over denominator 3 x end fraction fraction numerator 1 over denominator c o s open parentheses 3 x close parentheses end fraction equals 3 stack l i m with x rightwards arrow 0 below space fraction numerator s i n open parentheses 3 x close parentheses over denominator 3 x end fraction fraction numerator 1 over denominator c o s open parentheses 3 x close parentheses end fraction equals 3 stack l i m with x rightwards arrow 0 below space 1 fraction numerator 1 over denominator c o s open parentheses 0 close parentheses end fraction equals 3$