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Nilai

Nilai limit as x rightwards arrow infinity of invisible function application open parentheses square root of 9 x squared end root minus 6 x minus 1 minus square root of 9 x squared plus 6 x plus 1 end root close parentheses equals... 

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D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

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nilai dari adalah .

nilai dari limit as x rightwards arrow infinity of invisible function application open parentheses square root of 9 x squared end root minus 6 x minus 1 minus square root of 9 x squared plus 6 x plus 1 end root close parentheses adalah negative infinity.

Pembahasan

Ingatlah sifat limit berikut: . Selanjutnya, penyelesaian nilai limit tak hingga di atas adalah sebagai berikut: Dengan demikian, nilai dari adalah .

Ingatlah sifat limit berikut:

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 invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses g left parenthesis x right parenthesis plus-or-minus f left parenthesis x right parenthesis 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 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 invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank g end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank left parenthesis end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank right parenthesis end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus 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 invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank left parenthesis end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank right parenthesis end table.

Selanjutnya, penyelesaian nilai limit tak hingga di atas adalah sebagai berikut:

 table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of invisible function application open parentheses square root of 9 x squared end root minus 6 x minus 1 minus square root of 9 x squared plus 6 x plus 1 end root close parentheses end cell equals cell limit as x rightwards arrow infinity of invisible function application open parentheses 3 x minus 6 x minus 1 minus square root of open parentheses 3 x plus 1 close parentheses squared end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application open parentheses 3 x minus 6 x minus 1 minus open parentheses 3 x plus 1 close parentheses close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application open parentheses 3 x minus 6 x minus 1 minus 3 x minus 1 close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application open parentheses negative 6 x minus 2 close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application minus 6 x plus limit as x rightwards arrow infinity of invisible function application minus 2 end cell row blank equals cell negative limit as x rightwards arrow infinity of invisible function application 6 x minus limit as x rightwards arrow infinity of invisible function application 2 end cell row blank equals cell negative infinity minus 2 end cell row blank equals cell negative infinity. end cell end table 

Dengan demikian, nilai dari limit as x rightwards arrow infinity of invisible function application open parentheses square root of 9 x squared end root minus 6 x minus 1 minus square root of 9 x squared plus 6 x plus 1 end root close parentheses adalah negative infinity.

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