Tentukan nilai: X→∞lim(9x2+5−4x2−6x2−4+x2+3)

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Tentukan nilai:

$\style{font-size:14px}{\lim_{\mathrm X\rightarrow\infty}(\frac{\sqrt{\mathrm x^2-4}+\sqrt{\mathrm x^2+3}}{\sqrt{9\mathrm x^2+5}-\sqrt{4\mathrm x^2-6}})}$

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Pembahasan Soal:

Dengan menerapkan konsep limit fungsi mendekati takhingga.

Variabel $begin mathsize 14px style straight x end style$ dengan pangkat terbesar dari $begin mathsize 14px style fraction numerator square root of straight x squared minus 4 end root plus square root of straight x squared plus 3 end root over denominator square root of 9 straight x squared plus 5 end root minus square root of 4 straight x squared minus 6 end root end fraction end style$ adalah $begin mathsize 14px style square root of straight x squared end root end style$ maka pembilang dan penyebut pada limit fungsi dibagi oleh $begin mathsize 14px style square root of straight x squared end root end style$ . Sehingga diperoleh:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow infinity of left parenthesis fraction numerator square root of straight x squared minus 4 end root plus square root of straight x squared plus 3 end root over denominator square root of 9 straight x squared plus 5 end root minus square root of 4 straight x squared minus 6 end root end fraction right parenthesis end cell equals cell limit as straight x rightwards arrow infinity of left parenthesis fraction numerator begin display style fraction numerator square root of straight x squared minus 4 end root over denominator square root of straight x squared end root end fraction plus fraction numerator square root of straight x squared plus 3 end root over denominator square root of straight x squared end root end fraction end style over denominator begin display style fraction numerator square root of 9 straight x squared plus 5 end root over denominator square root of straight x squared end root end fraction minus fraction numerator square root of 4 straight x squared minus 6 end root over denominator square root of straight x squared end root end fraction end style end fraction right parenthesis end cell row blank equals cell limit as straight x rightwards arrow infinity of left parenthesis fraction numerator begin display style square root of fraction numerator straight x squared minus 4 over denominator straight x squared end fraction end root plus square root of fraction numerator begin display style straight x squared plus 3 end style over denominator begin display style straight x squared end style end fraction end root end style over denominator begin display style square root of fraction numerator 9 straight x squared plus 5 over denominator straight x squared end fraction end root minus square root of fraction numerator begin display style 4 straight x squared minus 6 end style over denominator begin display style straight x squared end style end fraction end root end style end fraction right parenthesis end cell row blank equals cell limit as straight x rightwards arrow infinity of left parenthesis fraction numerator begin display style square root of 1 minus 4 over straight x squared end root plus square root of 1 plus fraction numerator begin display style 3 end style over denominator begin display style straight x squared end style end fraction end root end style over denominator begin display style square root of 9 plus 5 over straight x squared end root minus square root of 4 minus fraction numerator begin display style 6 end style over denominator begin display style straight x squared end style end fraction end root end style end fraction right parenthesis end cell row blank equals cell left parenthesis fraction numerator begin display style square root of 1 minus 4 over infinity squared end root plus square root of 1 plus fraction numerator begin display style 3 end style over denominator begin display style infinity squared end style end fraction end root end style over denominator begin display style square root of 9 plus 5 over infinity squared end root minus square root of 4 minus fraction numerator begin display style 6 end style over denominator begin display style infinity squared end style end fraction end root end style end fraction right parenthesis end cell row blank equals cell fraction numerator begin display style square root of 1 minus 0 end root plus square root of 1 plus 0 end root end style over denominator begin display style square root of 9 plus 0 end root minus square root of 4 minus 0 end root end style end fraction right parenthesis end cell row blank equals cell fraction numerator begin display style 1 plus 1 end style over denominator begin display style 3 minus 2 end style end fraction end cell row blank equals 2 end table end style$

Jadi, Nilai dari $Error converting from MathML to accessible text.$ .

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Terakhir diupdate 07 Oktober 2021