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x → ∞ lim ​ ( ( x − 2 ) − x 2 + 8 x − 5 ​ )

  

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N. Puspita

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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses open parentheses x minus 2 close parentheses minus square root of x squared plus 8 x minus 5 end root close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table.

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Ingat! x → ∞ lim ​ ( a x 2 + b x + c ​ − p x 2 + q x + r ​ ) = ⎩ ⎨ ⎧ ​ ∞ , untuk a > p 2 a ​ b − q ​ , untuk a = p − ∞ , untuk a < p ​ ​ DIketahui , maka: dengan: Sehingga, nilai adalah: Jadi, .

Ingat!

 

DIketahui space limit as x rightwards arrow infinity of open parentheses open parentheses x minus 2 close parentheses minus square root of x squared plus 8 x minus 5 end root close parentheses, maka:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell space limit as x rightwards arrow infinity of open parentheses open parentheses x minus 2 close parentheses minus square root of x squared plus 8 x minus 5 end root close parentheses end cell row blank equals cell space limit as x rightwards arrow infinity of open parentheses square root of open parentheses x minus 2 close parentheses squared end root minus square root of x squared plus 8 x minus 5 end root close parentheses end cell row blank equals cell space limit as x rightwards arrow infinity of open parentheses square root of x squared minus 4 x plus 4 end root minus square root of x squared plus 8 x minus 5 end root close parentheses end cell end table 

dengan:

table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 1 comma space b equals negative 4 comma space c equals 4 end cell row p equals cell 1 comma space q equals 8 comma space r equals negative 5 end cell end table  

Sehingga, nilai space limit as x rightwards arrow infinity of open parentheses open parentheses x minus 2 close parentheses minus square root of x squared plus 8 x minus 5 end root close parentheses adalah:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell space limit as x rightwards arrow infinity of open parentheses open parentheses x minus 2 close parentheses minus square root of x squared plus 8 x minus 5 end root close parentheses end cell row blank equals cell space limit as x rightwards arrow infinity of open parentheses square root of x squared minus 4 x plus 4 end root minus square root of x squared plus 8 x minus 5 end root close parentheses end cell row blank equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator negative 4 minus 8 over denominator 2 square root of 1 end fraction end cell row blank equals cell fraction numerator negative 12 over denominator 2 end fraction end cell row blank equals cell negative 6 end cell end table 

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses open parentheses x minus 2 close parentheses minus square root of x squared plus 8 x minus 5 end root close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table.

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ahmad khairul umam

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Maria Aurelia Permata Sari

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