Función Coseno

En muchos casos, para poder resolver los límites de las funciones trigonométricas es aconsejable poder hacer uso de las famosas identidades trigonométricas.

stack l i m with x rightwards arrow 0 below space fraction numerator 1 minus cos squared left parenthesis x right parenthesis over denominator x squared end fraction equals stack l i m with x rightwards arrow 0 below space fraction numerator sin squared left parenthesis x right parenthesis over denominator x squared end fraction equals stack l i m with x rightwards arrow 0 below space fraction numerator s i n left parenthesis x right parenthesis over denominator x end fraction fraction numerator s i n left parenthesis x right parenthesis over denominator x end fraction equals 1

1 minus c o s squared left parenthesis x right parenthesis equals s i n squared left parenthesis x right parenthesis

stack l i m with x rightwards arrow 0 below space fraction numerator sin squared left parenthesis x right parenthesis plus c o s squared left parenthesis x right parenthesis minus 3 x squared over denominator x squared plus 4 x end fraction equals stack l i m with x rightwards arrow 0 below space fraction numerator 1 minus 3 x squared over denominator x squared plus 4 x end fraction equals negative 3 over 1 equals negative 3

s i n squared left parenthesis x right parenthesis plus c o s squared left parenthesis x right parenthesis equals 1

El cambio de variable también puede resultar ser un buen método a la hora de resolver funciones trigonométricas.

stack l i m with x rightwards arrow straight pi over 2 below space fraction numerator straight pi over 2 minus x over denominator c o s left parenthesis x right parenthesis end fraction equals stack l i m with u rightwards arrow 0 below space fraction numerator u over denominator c o s left parenthesis straight pi over 2 minus u right parenthesis end fraction equals stack l i m with u rightwards arrow 0 below space fraction numerator u over denominator sin left parenthesis u right parenthesis end fraction equals stack l i m with u rightwards arrow 0 below space fraction numerator u over denominator s i n left parenthesis u right parenthesis end fraction
stack l i m with u rightwards arrow 0 below space fraction numerator u over denominator s i n left parenthesis u right parenthesis end fraction equals stack l i m with u rightwards arrow 0 below space open parentheses fraction numerator s i n left parenthesis u right parenthesis over denominator u end fraction close parentheses to the power of negative 1 end exponent equals 1

u equals straight pi over 2 minus x space semicolon space
c o s left parenthesis straight pi over 2 minus u right parenthesis equals sin left parenthesis u right parenthesis semicolon
fraction numerator u over denominator s i n left parenthesis u right parenthesis end fraction equals open parentheses fraction numerator s i n left parenthesis u right parenthesis over denominator u end fraction close parentheses to the power of negative 1 end exponent

 

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Levis Wilson Estevez

Licenciado en Fisica Nuclear.

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