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Pertanyaan

x → − 2 lim ​ x 3 + x 2 + 4 x 3 + 8 ​ = ....

 

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

.

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow negative 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x cubed plus 8 over denominator x cubed plus x squared plus 4 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 3 over 2 end cell end table end style.

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Pembahasan

Pembahasan

Perhatikan perhitungan berikut! Karena hasil dari limit ketika disubstitusikan merupakan bilangan tak tentu , maka kita lakukan pemfaktoran pada bentuk limit tersebut sebagai berikut: Jadi, .

Perhatikan perhitungan berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of fraction numerator x cubed plus 8 over denominator x cubed plus x squared plus 4 end fraction end cell equals cell fraction numerator left parenthesis negative 2 right parenthesis cubed plus 8 over denominator left parenthesis negative 2 right parenthesis cubed plus left parenthesis negative 2 right parenthesis squared plus 4 end fraction end cell row blank equals cell fraction numerator negative 8 plus 8 over denominator negative 8 plus 4 plus 4 end fraction end cell row blank equals cell 0 over 0 end cell end table 

Karena hasil dari limit ketika disubstitusikan begin mathsize 14px style x equals negative 2 end style merupakan bilangan tak tentubegin mathsize 14px style 0 over 0 end style, maka kita lakukan pemfaktoran pada bentuk limit tersebut sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of fraction numerator x cubed plus 8 over denominator x cubed plus x squared plus 4 end fraction end cell equals cell limit as x rightwards arrow negative 2 of fraction numerator left parenthesis x plus 2 right parenthesis left parenthesis x squared minus 2 x plus 4 right parenthesis over denominator left parenthesis x plus 2 right parenthesis left parenthesis x squared minus x plus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator left parenthesis x squared minus 2 x plus 4 right parenthesis over denominator left parenthesis x squared minus x plus 2 right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis negative 2 right parenthesis squared minus 2 times left parenthesis negative 2 right parenthesis plus 4 over denominator left parenthesis negative 2 right parenthesis squared minus left parenthesis negative 2 right parenthesis plus 2 end fraction end cell row blank equals cell fraction numerator 4 plus 4 plus 4 over denominator 4 plus 2 plus 2 end fraction end cell row blank equals cell 12 over 8 end cell row blank equals cell 3 over 2 end cell end table 

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 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x cubed plus 8 over denominator x cubed plus x squared plus 4 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 3 over 2 end cell end table end style.

Latihan Bab

Konsep Kilat

Konsep Limit

Sifat Limit

Limit Fungsi Aljabar

48

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Hitunglah limit fungsi berikut! c. x → 1 lim ​ 3 x ​ − 1 x − 1 ​

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