Pertanyaan

Tentukan nilai limit x → 3 lim ( x − 3 ) ( x − 3 ) ( x + 3 ) !

Tentukan nilai limit $x \to 3 lim \frac{( x - 3 ) ( x + 3 )}{( x - 3 )}$ !

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Habis dalam

Klaim

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai limit adalah .

nilai limit $limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 3 close parentheses open parentheses square root of x plus square root of 3 close parentheses over denominator open parentheses square root of x minus square root of 3 close parentheses end fraction$ adalah

Pembahasan

Langkah pertama untuk menentukan nilai limit fungsi adalah merasionalkan bentuk akarnya sebagai berikut. Kemudian, dengan menggunakan metode substitusi, nilai limit tersebut sebagai berikut. Dengan demikian,nilai limit adalah .

Langkah pertama untuk menentukan nilai limit fungsi $limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 3 close parentheses open parentheses square root of x plus square root of 3 close parentheses over denominator open parentheses square root of x minus square root of 3 close parentheses end fraction$ adalah merasionalkan bentuk akarnya 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 open parentheses x minus 3 close parentheses open parentheses square root of x plus square root of 3 close parentheses over denominator open parentheses square root of x minus square root of 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 3 close parentheses open parentheses square root of x plus square root of 3 close parentheses over denominator open parentheses square root of x minus square root of 3 close parentheses end fraction times fraction numerator open parentheses square root of x plus square root of 3 close parentheses over denominator 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 fraction numerator open parentheses x minus 3 close parentheses open parentheses square root of x plus square root of 3 close parentheses open parentheses square root of x plus square root of 3 close parentheses over denominator open parentheses square root of x minus square root of 3 close parentheses 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 fraction numerator open parentheses x minus 3 close parentheses open parentheses square root of x plus square root of 3 close parentheses squared over denominator open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator 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 squared over denominator up diagonal strike open parentheses x minus 3 close parentheses end strike end fraction end cell row blank equals cell limit as x rightwards arrow 3 of open parentheses square root of x plus square root of 3 close parentheses squared end cell end table$

Kemudian, dengan menggunakan metode substitusi, nilai limit tersebut sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 3 close parentheses open parentheses square root of x plus square root of 3 close parentheses over denominator open parentheses square root of x minus square root of 3 close parentheses end fraction end cell equals cell limit as x rightwards arrow 3 of open parentheses square root of x plus square root of 3 close parentheses squared end cell row blank equals cell open parentheses square root of 3 plus square root of 3 close parentheses squared end cell row blank equals cell open parentheses 2 square root of 3 close parentheses squared end cell row blank equals cell 4 times 3 end cell row blank equals 12 end table$

Dengan demikian, nilai limit $limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 3 close parentheses open parentheses square root of x plus square root of 3 close parentheses over denominator open parentheses square root of x minus square root of 3 close parentheses end fraction$ adalah .