Resolución de Límites Trigonométricos

Para resolver límites trigonométricos solo basta con conocer las identidades trigonométricas y ciertos límites que no vamos a demostrar en este curso.

$f left parenthesis x right parenthesis equals fraction numerator sin open parentheses 5 x close parentheses over denominator 2 x end fraction stack l i m with x rightwards arrow 0 below space fraction numerator s i n open parentheses 5 x close parentheses over denominator 2 x end fraction equals stack l i m with x rightwards arrow 0 below space fraction numerator 5 x space begin display style fraction numerator sin open parentheses 5 x close parentheses over denominator 5 x end fraction end style over denominator 2 x end fraction equals stack l i m with x rightwards arrow 0 below space fraction numerator 5 space begin display style fraction numerator s i n open parentheses 5 x close parentheses over denominator 5 x end fraction end style over denominator 2 end fraction equals 5 over 2 stack l i m with x rightwards arrow 0 below space fraction numerator s i n open parentheses 5 x close parentheses over denominator 5 x end fraction stack l i m with x rightwards arrow 0 below space fraction numerator s i n open parentheses 5 x close parentheses over denominator 2 x end fraction equals 5 over 2 stack l i m with x rightwards arrow 0 below space fraction numerator s i n open parentheses 5 x close parentheses over denominator 5 x end fraction equals 5 over 2 stack l i m with x rightwards arrow 0 below space fraction numerator s i n open parentheses 5 x close parentheses over denominator 5 x end fraction equals 1 E n space g e n e r a l colon stack l i m with x rightwards arrow 0 below space fraction numerator s i n open parentheses a x close parentheses over denominator a x end fraction equals 1 space semicolon space d o n d e space a element of space R$