Repaso del contenido impartido

Haciendo un resumen del contenido impartido podemos decir que en el método de evaluación de límite se procede a evaluar en la función que deseamos hallarle el límite el número, sea cual sea, al que tiende la variable x de la función.

 

Ejemplos:

stack l i m with x rightwards arrow 4 below space f left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 4 below space 10.013 equals 10.013
stack l i m with x rightwards arrow 4 below space g left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 4 below space 3.1415926.... equals 3.1415926....

g(x)=76.34 ; h(x)= 34

stack l i m with x rightwards arrow 3 below space fraction numerator g left parenthesis x right parenthesis over denominator h left parenthesis x right parenthesis end fraction equals fraction numerator stack l i m with x rightwards arrow 3 below space g left parenthesis x right parenthesis space over denominator stack l i m with x rightwards arrow 3 below space h left parenthesis x right parenthesis end fraction equals fraction numerator stack l i m with x rightwards arrow 3 below space 76.34 over denominator stack l i m with x rightwards arrow 3 below space 34 end fraction equals fraction numerator 76.34 over denominator 34 end fraction approximately equal to 2.2453

stack l i m with x rightwards arrow 4.3 below 4 space open parentheses square root of 45 space plus space 3 comma 4 squared close parentheses x equals stack space 4 open parentheses square root of 45 space plus space 3 comma 4 squared close parentheses l i m with space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space x rightwards arrow 4.3 below x equals 4 open parentheses square root of 45 space plus space 3 comma 4 squared close parentheses cross times space left parenthesis 4.3 right parenthesis

f left parenthesis x right parenthesis equals x squared plus x to the power of 4
stack l i m with x rightwards arrow 2 below space f left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 2 below space x squared plus x to the power of 4 equals stack l i m with x rightwards arrow 2 below space left parenthesis 2 right parenthesis squared plus left parenthesis 2 right parenthesis to the power of 4 equals left parenthesis 2 right parenthesis squared plus left parenthesis 2 right parenthesis to the power of 4 equals 4 space plus space 16 equals 20

g left parenthesis x right parenthesis equals 1 over x squared plus x cubed
stack l i m with x rightwards arrow 3.14 below space g left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 3.14 below space space 1 over x squared plus x cubed space equals stack l i m with x rightwards arrow 3.14 below space space fraction numerator 1 over denominator left parenthesis 3.14 right parenthesis squared end fraction plus left parenthesis 3.14 right parenthesis cubed equals stack l i m with x rightwards arrow 3.14 below space space fraction numerator 1 over denominator 9.8596 end fraction plus 30.959144 equals stack l i m with x rightwards arrow 3.14 below space space 31.060568
stack l i m with x rightwards arrow 3.14 below space space 31.060568 equals space space 31.060568

h left parenthesis x right parenthesis equals space x s i n left parenthesis x right parenthesis
stack l i m with x rightwards arrow straight pi over 2 below space h left parenthesis x right parenthesis equals limit as straight x rightwards arrow straight pi over 2 of space space x s i n left parenthesis x right parenthesis space equals stack l i m with straight x rightwards arrow straight pi over 2 below space straight pi over 2 s i n left parenthesis straight pi over 2 right parenthesis equals straight pi over 2 s i n left parenthesis straight pi over 2 right parenthesis equals straight pi over 2

K left parenthesis x right parenthesis equals e to the power of x sin open parentheses 2 x plus straight pi over 2 close parentheses
stack l i m with x rightwards arrow 0 below space K left parenthesis x right parenthesis equals stack l i m with x rightwards arrow 0 below space e to the power of x s i n open parentheses 2 x plus straight pi over 2 close parentheses equals stack l i m with x rightwards arrow 0 below space e to the power of 0 s i n open parentheses 2 left parenthesis 0 right parenthesis plus straight pi over 2 close parentheses equals e to the power of 0 s i n open parentheses 2 left parenthesis 0 right parenthesis plus straight pi over 2 close parentheses equals 1 cross times s i n open parentheses 2 left parenthesis 0 right parenthesis plus straight pi over 2 close parentheses equals 1 cross times s i n open parentheses straight pi over 2 close parentheses
1 cross times s i n open parentheses straight pi over 2 close parentheses equals 1 cross times 1 equals 1

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Levis Wilson Estevez

Licenciado en Fisica Nuclear.

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