Pertanyaan

Nilai dari x → ∞ lim x − 4 − 9 x + 2 x − 5 + 4 x − 7 = ...

Nilai dari $x \to \infty lim \frac{x - 5 + 4 x - 7}{x - 4 - 9 x + 2} = ...$

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Jawaban terverifikasi

Jawaban

nilai .

nilai $limit as straight x rightwards arrow infinity of fraction numerator square root of x minus 5 end root plus square root of 4 x minus 7 end root over denominator square root of x minus 4 end root minus square root of 9 x plus 2 end root end fraction equals 3 over 8$ .

Pembahasan

Dengan mengalikan pecahan pada limit dengan akar sekawannya, maka diperoleh: Jadi, nilai .

Dengan mengalikan pecahan pada limit dengan akar sekawannya, maka diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow infinity of fraction numerator square root of x minus 5 end root plus square root of 4 x minus 7 end root over denominator square root of x minus 4 end root minus square root of 9 x plus 2 end root end fraction end cell equals cell limit as straight x rightwards arrow infinity of fraction numerator square root of x minus 5 end root plus square root of 4 x minus 7 end root over denominator square root of x minus 4 end root minus square root of 9 x plus 2 end root end fraction cross times fraction numerator square root of x minus 4 end root plus square root of 9 x plus 2 end root over denominator square root of x minus 4 end root plus square root of 9 x plus 2 end root end fraction cross times fraction numerator square root of x minus 5 end root minus square root of 4 x minus 7 end root over denominator square root of x minus 5 end root minus square root of 4 x minus 7 end root end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator left parenthesis x minus 5 right parenthesis minus left parenthesis 4 x minus 7 right parenthesis over denominator left parenthesis x minus 4 right parenthesis minus left parenthesis 9 x plus 2 right parenthesis end fraction cross times fraction numerator square root of x minus 4 end root plus square root of 9 x plus 2 end root over denominator square root of x minus 5 end root minus square root of 4 x minus 7 end root end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator open parentheses negative 3 x plus 2 close parentheses open parentheses square root of x minus 4 end root plus square root of 9 x plus 2 end root close parentheses over denominator open parentheses negative 8 x minus 6 close parentheses open parentheses square root of x minus 5 end root minus square root of 4 x minus 7 end root close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator open parentheses begin display style fraction numerator negative 3 x over denominator x end fraction end style plus begin display style 2 over x end style close parentheses open parentheses square root of begin display style x over x end style minus begin display style 4 over x end style end root plus square root of begin display style fraction numerator 9 x over denominator x end fraction end style plus begin display style 2 over x end style end root close parentheses over denominator open parentheses begin display style fraction numerator negative 8 x over denominator x end fraction end style minus begin display style 6 over x end style close parentheses open parentheses square root of begin display style x over x end style minus begin display style 5 over x end style end root minus square root of begin display style fraction numerator 4 x over denominator x end fraction end style minus begin display style 7 over x end style end root close parentheses end fraction end cell row blank equals cell fraction numerator negative 3 plus 0 open parentheses square root of 1 plus square root of 9 close parentheses over denominator negative 8 minus 0 open parentheses square root of 1 plus square root of 4 close parentheses end fraction end cell row blank equals cell 3 over 8 end cell end table$

Jadi, nilai $limit as straight x rightwards arrow infinity of fraction numerator square root of x minus 5 end root plus square root of 4 x minus 7 end root over denominator square root of x minus 4 end root minus square root of 9 x plus 2 end root end fraction equals 3 over 8$ .