Pertanyaan

Tentukan nilai limit dari x → 2 lim x − 2 3 x − 6 = ....

Tentukan nilai limit dari $x \to 2 lim \frac{3 x - 6}{x - 2}$ = ....

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

nilai limit dari adalah .

nilai limit dari $limit as x rightwards arrow 2 of fraction numerator square root of 3 x end root minus square root of 6 over denominator square root of x minus square root of 2 end fraction$ adalah

Pembahasan

Untuk menentukan nilai limit dari dengan menggunakan aturan L'Hospital yaitu : Jika maka Sehingga diperoleh : Jadi,nilai limit dari adalah .

Untuk menentukan nilai limit dari $limit as x rightwards arrow 2 of fraction numerator square root of 3 x end root minus square root of 6 over denominator square root of x minus square root of 2 end fraction$ dengan menggunakan aturan L'Hospital yaitu :

Jika $limit as x rightwards arrow a of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction$ maka $limit as x rightwards arrow a of fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction equals fraction numerator f apostrophe left parenthesis a right parenthesis over denominator g apostrophe left parenthesis a right parenthesis end fraction$

Sehingga diperoleh :

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

Jadi, nilai limit dari $limit as x rightwards arrow 2 of fraction numerator square root of 3 x end root minus square root of 6 over denominator square root of x minus square root of 2 end fraction$ adalah .