Pertanyaan

Tentukan hasil dari x → 3 lim x − 3 6 + x − 3 x

Tentukan hasil dari $x \to 3 lim \frac{6 + x - 3 x}{x - 3}$

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Klaim

J. Joko

Master Teacher

Jawaban terverifikasi

Jawaban

nilai .

nilai $begin mathsize 14px style limit as x rightwards arrow 3 of invisible function application fraction numerator square root of 6 plus x end root minus square root of 3 x end root over denominator x minus 3 end fraction equals negative 1 third end style$ .

Pembahasan

Jika dijumpai limit dengan bentuk akar dan tidak dapat difaktorkan secara langsung, maka kalikan dengan bentuk sekawannya. Jadi nilai .

Jika dijumpai limit dengan bentuk akar dan tidak dapat difaktorkan secara langsung, maka kalikan dengan bentuk sekawannya.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of invisible function application fraction numerator square root of 6 plus x end root minus square root of 3 x end root over denominator x minus 3 end fraction end cell equals cell limit as x rightwards arrow 3 of invisible function application fraction numerator square root of 6 plus x end root minus square root of 3 x end root over denominator x minus 3 end fraction times fraction numerator square root of 6 plus x end root plus square root of 3 x end root over denominator square root of 6 plus x end root plus square root of 3 x end root end fraction end cell row blank equals cell limit as x rightwards arrow 3 of invisible function application fraction numerator 6 plus x minus 3 x over denominator left parenthesis x minus 3 right parenthesis open parentheses square root of 6 plus x end root plus square root of 3 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of invisible function application fraction numerator 6 minus 2 x over denominator left parenthesis x minus 3 right parenthesis left parenthesis square root of 6 plus x end root plus square root of 3 x end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 3 of invisible function application fraction numerator negative 2 up diagonal strike left parenthesis x minus 3 right parenthesis end strike over denominator up diagonal strike left parenthesis x minus 3 right parenthesis end strike left parenthesis square root of 6 plus x end root plus square root of 3 x end root right parenthesis end fraction end cell row blank equals cell fraction numerator negative 2 over denominator square root of 6 plus 3 end root plus square root of 3 left parenthesis 3 right parenthesis end root end fraction end cell row blank equals cell fraction numerator negative 2 over denominator 6 end fraction end cell row blank equals cell negative 1 third end cell end table end style$

Jadi nilai $begin mathsize 14px style limit as x rightwards arrow 3 of invisible function application fraction numerator square root of 6 plus x end root minus square root of 3 x end root over denominator x minus 3 end fraction equals negative 1 third end style$ .