Pertanyaan

x → 2 lim x − 2 2 + x − x 2

$x \to 2 lim \frac{2 + x - x ^{2}}{x - 2}$

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai

nilai $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 plus x minus x squared over denominator square root of x minus square root of 2 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table$

Pembahasan

Nilai limit fungsi tersebut dapat ditentukan dengan metode perkalian akar sekawan sebagai berikut. Dengan demikian, nilai

Nilai limit fungsi tersebut dapat ditentukan dengan metode perkalian akar sekawan sebagai berikut.

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

Dengan demikian, nilai $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 plus x minus x squared over denominator square root of x minus square root of 2 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table$