Pertanyaan

Nilai x → 3 lim x − 5 x − 6 3 − x = ...

Nilai $x \to 3 lim \frac{3 - x}{x - 5 x - 6} = ...$

8 dari 10 siswa nilainya naik

dengan paket belajar pilihan

Habis dalam

Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

Nilai adalah .

Nilai $limit as x rightwards arrow 3 of fraction numerator 3 minus x over denominator x minus square root of 5 x minus 6 end root end fraction$ adalah negative 6

Pembahasan

Rasionalkan penyebutnya dengan perkalian akar sekawan : Maka : Jadi,Nilai adalah .

Rasionalkan penyebutnya dengan perkalian akar sekawan :

left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis equals a squared minus b squared

Maka :

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of fraction numerator 3 minus x over denominator x minus square root of 5 x minus 6 end root end fraction cross times fraction numerator x plus square root of 5 x minus 6 end root over denominator x plus square root of 5 x minus 6 end root end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses 3 minus x close parentheses open parentheses x plus square root of 5 x minus 6 end root close parentheses over denominator x squared minus 5 x plus 6 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator negative open parentheses x minus 3 close parentheses open parentheses x plus square root of 5 x minus 6 end root close parentheses over denominator x squared minus 5 x plus 6 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator negative up diagonal strike open parentheses x minus 3 close parentheses end strike open parentheses x plus square root of 5 x minus 6 end root close parentheses over denominator up diagonal strike left parenthesis x minus 3 right parenthesis end strike left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator negative open parentheses x plus square root of 5 x minus 6 end root close parentheses over denominator left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell negative fraction numerator 3 plus square root of 5 left parenthesis 3 right parenthesis minus 6 end root over denominator 3 minus 2 end fraction end cell row blank equals cell negative fraction numerator 3 plus square root of 15 minus 6 end root over denominator 1 end fraction end cell row blank equals cell fraction numerator 3 plus square root of 9 over denominator 1 end fraction end cell row blank equals cell negative fraction numerator 3 plus 3 over denominator 1 end fraction end cell row blank equals cell negative 6 end cell end table$

Jadi, Nilai $limit as x rightwards arrow 3 of fraction numerator 3 minus x over denominator x minus square root of 5 x minus 6 end root end fraction$ adalah negative 6 .