Ejemplos de Límites. Método de Evaluación de Límites II

En esta lección vamos a introducir el método de evaluación para funciones de variable real más complejas.Como en la lección anterior el método de evaluación consiste en sustituir en  la función a la cual le queremos hallar el límite el valor al cual tiende la variable x.

 

Ejemplos.

c left parenthesis x right parenthesis equals 1 over x
stack l i m with x rightwards arrow 4 below space c left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 4 below space 1 over x equals stack l i m with x rightwards arrow 4 below space 1 fourth equals 1 fourth equals 0.25

d left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 2 x end fraction
stack l i m with x rightwards arrow 4 below space d left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 4 below space fraction numerator 1 over denominator x squared plus 2 x end fraction equals stack l i m with x rightwards arrow 4 below fraction numerator 1 over denominator 4 squared plus 2 left parenthesis 4 right parenthesis end fraction equals stack l i m with x rightwards arrow 4 below fraction numerator 1 over denominator 16 plus 8 end fraction equals fraction numerator 1 over denominator 16 plus 8 end fraction equals 1 over 24 equals 0.041

e left parenthesis x right parenthesis equals fraction numerator x cubed plus 4 over denominator x squared plus 7 end fraction
stack l i m space with x rightwards arrow 2 below space e left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 2 below fraction numerator x cubed plus 4 over denominator x squared plus 7 end fraction equals stack l i m with x rightwards arrow 2 below fraction numerator 2 cubed plus 4 over denominator 2 squared plus 7 end fraction equals stack l i m with x rightwards arrow 2 below fraction numerator 8 plus 4 over denominator 4 plus 7 end fraction equals stack l i m with x rightwards arrow 2 below 12 over 11 equals 12 over 11 equals 1.09

f left parenthesis x right parenthesis equals fraction numerator x squared plus cube root of x over denominator x cos open parentheses x close parentheses end fraction
stack l i m with x rightwards arrow 3 below space f left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 3 below space fraction numerator x squared plus cube root of x over denominator x c o s open parentheses x close parentheses end fraction equals stack l i m with x rightwards arrow 3 below space fraction numerator 3 squared plus cube root of 3 over denominator 3 c o s open parentheses 3 close parentheses end fraction equals stack l i m with x rightwards arrow 3 below fraction numerator 10.442 over denominator 3 c o s open parentheses 3 close parentheses end fraction equals stack l i m with x rightwards arrow 3 below fraction numerator 10.442 over denominator negative 3 end fraction
stack l i m with x rightwards arrow 3 below fraction numerator 10.442 over denominator negative 3 end fraction equals fraction numerator 10.442 over denominator negative 3 end fraction approximately equal to negative 3.48

g left parenthesis x right parenthesis equals square root of fraction numerator x cubed plus square root of x over denominator e to the power of x sin open parentheses x close parentheses end fraction end root
stack l i m with x rightwards arrow straight pi over 2 below g left parenthesis x right parenthesis equals stack l i m with x rightwards arrow straight pi over 2 below square root of fraction numerator x cubed plus square root of x over denominator e to the power of x s i n open parentheses x close parentheses end fraction end root equals stack l i m with x rightwards arrow straight pi over 2 below square root of fraction numerator straight pi over 2 cubed plus square root of straight pi over 2 end root over denominator e to the power of straight pi over 2 end exponent s i n open parentheses straight pi over 2 close parentheses end fraction end root equals stack l i m with x rightwards arrow straight pi over 2 below square root of fraction numerator straight pi over 2 cubed plus square root of straight pi over 2 end root over denominator e to the power of straight pi over 2 end exponent s i n open parentheses straight pi over 2 close parentheses end fraction end root equals stack l i m with x rightwards arrow straight pi over 2 below square root of fraction numerator 5.13 over denominator e to the power of straight pi over 2 end exponent s i n open parentheses straight pi over 2 close parentheses end fraction end root equals
stack l i m with x rightwards arrow straight pi over 2 below square root of fraction numerator 5.13 over denominator 4.81 end fraction end root equals square root of fraction numerator 5.13 over denominator 4.81 end fraction end root approximately equal to 1.033

h left parenthesis x right parenthesis equals integral 1 over x
stack l i m with x rightwards arrow 2 below space h left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 2 below space integral 1 over x equals stack l i m with x rightwards arrow 2 below space ln open parentheses x close parentheses equals stack l i m with x rightwards arrow 2 below space l n open parentheses 2 close parentheses equals l n open parentheses 2 close parentheses equals 0.693

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Levis Wilson Estevez

Licenciado en Fisica Nuclear.

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