Pertanyaan

Nilai x → ∞ lim ( x 2 + 3 x + 5 − x + 2 ) = ...

Nilai $x \to \infty lim (x^{2} + 3 x + 5 - x + 2) = ...$

8 dari 10 siswa nilainya naik

dengan paket belajar pilihan

Habis dalam

Klaim

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

$equals limit as x rightwards arrow infinity of open parentheses square root of x squared plus 3 x plus 5 end root space minus x plus 2 close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of x squared plus 3 x plus 5 end root space minus open parentheses x minus 2 close parentheses close parentheses equals limit as x rightwards arrow infinity of open parentheses square root of x squared plus 3 x plus 5 end root space minus left parenthesis x minus 2 right parenthesis close parentheses cross times fraction numerator square root of x squared plus 3 x plus 5 end root space plus left parenthesis x minus 2 right parenthesis over denominator square root of x squared plus 3 x plus 5 end root space plus left parenthesis x minus 2 right parenthesis end fraction equals limit as x rightwards arrow infinity of fraction numerator x squared plus 3 x plus 5 space minus left parenthesis x minus 2 right parenthesis squared over denominator square root of x squared plus 3 x plus 5 end root space plus left parenthesis x minus 2 right parenthesis end fraction equals limit as x rightwards arrow infinity of fraction numerator x squared plus 3 x plus 5 space minus x squared plus 4 x minus 4 over denominator square root of x squared plus 3 x plus 5 end root space plus left parenthesis x minus 2 right parenthesis end fraction equals limit as x rightwards arrow infinity of fraction numerator 7 x plus 1 over denominator square root of x squared plus 3 x plus 5 end root space plus left parenthesis x minus 2 right parenthesis end fraction cross times fraction numerator begin display style 1 over x end style over denominator begin display style 1 over x end style end fraction equals limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 7 x over denominator x end fraction end style plus begin display style 1 over x end style over denominator square root of begin display style x squared over x squared end style plus begin display style fraction numerator 3 x over denominator x squared end fraction end style plus begin display style 5 over x squared end style end root space plus open parentheses begin display style x over x end style minus begin display style 2 over x end style close parentheses end fraction equals limit as x rightwards arrow infinity of fraction numerator 7 plus begin display style 1 over x end style over denominator square root of 1 plus 3 over x plus 5 over x squared end root space plus open parentheses 1 minus 2 over x close parentheses end fraction equals fraction numerator 7 plus begin display style 1 over infinity end style over denominator square root of 1 plus 3 over infinity plus 5 over infinity end root space plus open parentheses 1 minus 2 over infinity close parentheses end fraction equals fraction numerator 7 plus 0 over denominator square root of 1 plus 0 plus 0 end root plus 1 minus 0 end fraction equals fraction numerator 7 over denominator 1 plus 1 end fraction equals 7 over 2$