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Tentukan nilai dari

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Tentukan nilai dari begin mathsize 14px style limit as x rightwards arrow negative 1 of invisible function application fraction numerator x cubed minus 3 x squared minus 4 x over denominator x cubed minus x squared minus 2 x end fraction end style 

Pembahasan Video:

Pembahasan Soal:

Subtitusi nilai x:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 1 of fraction numerator x cubed minus 3 x squared minus 4 x over denominator x cubed minus x squared minus 2 x end fraction end cell equals cell fraction numerator left parenthesis negative 1 right parenthesis cubed minus 3 times left parenthesis negative 1 right parenthesis squared minus 4 times left parenthesis negative 1 right parenthesis over denominator left parenthesis negative 1 right parenthesis cubed minus left parenthesis negative 1 right parenthesis squared minus 2 times left parenthesis negative 1 right parenthesis end fraction end cell row blank equals cell fraction numerator negative 1 minus 3 plus 4 over denominator negative 1 minus 1 plus 2 end fraction end cell row blank equals cell 0 over 0 end cell end table end style

Karena hasil tidak terdefinisi, maka difaktorkan sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 1 of fraction numerator x cubed minus 3 x squared minus 4 x over denominator x cubed minus x squared minus 2 x end fraction end cell equals cell limit as x rightwards arrow negative 1 of fraction numerator x left parenthesis x squared minus 3 x minus 4 right parenthesis over denominator x left parenthesis x squared minus x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 1 of fraction numerator x squared minus 3 x minus 4 over denominator x squared minus x minus 2 end fraction end cell row blank equals cell limit as x rightwards arrow negative 1 of fraction numerator left parenthesis x plus 1 right parenthesis left parenthesis x minus 4 right parenthesis over denominator left parenthesis x plus 1 right parenthesis left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 1 of fraction numerator x minus 4 over denominator x minus 2 end fraction end cell row blank equals cell fraction numerator negative 1 minus 4 over denominator negative 1 minus 2 end fraction end cell row blank equals cell fraction numerator negative 5 over denominator negative 3 end fraction end cell row blank equals cell 5 over 3 end cell end table end style 

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow negative 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x cubed minus 3 x squared minus 4 x over denominator x cubed minus x squared minus 2 x end fraction 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 5 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank end table end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Agustus 2021

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