Pertanyaan

x → 3 lim x − 3 ( x − 3 ) = ... .

$x \to 3 lim \frac{( x - 3 )}{x - 3} = ...$ .

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh $limit as x rightwards arrow 3 of space fraction numerator open parentheses square root of x minus square root of 3 close parentheses over denominator x minus 3 end fraction equals 1 over 6 square root of 3$ .

Pembahasan

Limit fungsi dengan metode mengalikan akar sekawan. Cek limit terlebih dahulu jika nilai limit maka harus disederhanakan dengan pemfaktoran atau mengalikan dengan akar sekawan. Karena nilai limit , dan terdapat bentuk akar maka disederhanakan dengan cara mengalikan dengan akar sekawan. Jadi, diperoleh .

Limit fungsi dengan metode mengalikan akar sekawan.

Cek limit terlebih dahulu jika nilai limit 0 over 0 maka harus disederhanakan dengan pemfaktoran atau mengalikan dengan akar sekawan.

$limit as x rightwards arrow 3 of space fraction numerator open parentheses square root of x minus square root of 3 close parentheses over denominator x minus 3 end fraction equals fraction numerator open parentheses square root of 3 minus square root of 3 close parentheses over denominator 3 minus 3 end fraction equals 0 over 0$

Karena nilai limit 0 over 0 , dan terdapat bentuk akar maka disederhanakan dengan cara mengalikan dengan akar sekawan.

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

Jadi, diperoleh $limit as x rightwards arrow 3 of space fraction numerator open parentheses square root of x minus square root of 3 close parentheses over denominator x minus 3 end fraction equals 1 over 6 square root of 3$ .