x→3limx−3(x−3)(x+3)=....

Pertanyaan

$begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis open parentheses square root of x plus square root of 3 close parentheses over denominator square root of x minus square root of 3 end fraction equals.... end style$

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Cara paling dasar dalam menentukan nilai limit fungsi aljabar adalah dengan metode substitusi. Apabila hasil dari substitusi tersebut menghasilkan bentuk tak tentu, penyelesaian limit harus menggunakan metode lain, yaitu pemfaktoran atau perkalian akar sekawan.

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

Hasil dari substitusi tersebut merupakan bentuk tak tentu sehingga penyelesaian soal limit tersebut menggunakan perkalian akar sekawan sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis square root of x plus square root of 3 right parenthesis over denominator square root of x minus square root of 3 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis square root of x plus square root of 3 right parenthesis left parenthesis square root of x plus square root of 3 right parenthesis over denominator open parentheses square root of x minus square root of 3 close parentheses left parenthesis square root of x plus square root of 3 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis square root of x plus square root of 3 right parenthesis left parenthesis square root of x plus square root of 3 right parenthesis over denominator left parenthesis x minus 3 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 3 of left parenthesis square root of x plus square root of 3 right parenthesis squared space end cell row blank equals cell open parentheses square root of 3 plus square root of 3 close parentheses squared end cell row blank equals cell open parentheses 2 square root of 3 close parentheses squared end cell row blank equals 12 end table$

Dengan demikian, nilai dari $table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis square root of x plus square root of 3 right parenthesis over denominator square root of x minus square root of 3 end fraction end cell equals 12 end table$