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Nilai x→−3lim​5x+152x2+6x​ adalah ...

Pertanyaan

Nilai begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction end style adalah ...

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction end style adalah size 14px minus size 14px 1 size 14px 1 over size 14px 5.

Pembahasan

size 14px x size 14px equals size 14px minus size 14px 3 disubtitusikan pada limit tersebut

begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction equals limit as x rightwards arrow negative 3 of fraction numerator 2 left parenthesis negative 3 right parenthesis squared plus 6 left parenthesis negative 3 right parenthesis over denominator 5 left parenthesis negative 3 right parenthesis plus 15 end fraction equals 0 over 0 end style 

Karena menghasilkan limit tak tentu, maka nilai limit bisa ditentukan dengan metode pemfaktoran sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction end cell equals cell limit as x rightwards arrow negative 3 of fraction numerator 2 x up diagonal strike left parenthesis x plus 3 right parenthesis end strike over denominator 5 up diagonal strike left parenthesis x plus 3 right parenthesis end strike end fraction end cell row cell 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 end cell equals cell fraction numerator 2 left parenthesis negative 3 right parenthesis over denominator 5 end fraction end cell row cell 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 end cell equals cell fraction numerator negative 6 over denominator 5 end fraction end cell row cell 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 end cell equals cell negative 1 1 fifth end cell end table end style 

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction end style adalah size 14px minus size 14px 1 size 14px 1 over size 14px 5.

158

5.0 (10 rating)

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