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Hasil dari  adalah ...

Hasil dari begin mathsize 14px style limit as x rightwards arrow infinity of space open parentheses 9 x plus 3 close parentheses squared over open parentheses 3 x plus 8 close parentheses squared end style adalah ...

Jawaban:

Dengan menggunakan konsep limit tak hingga, uraikan terlebih dahulu bentuk aljabar tersebut, kemudian bagi semua suku dengan variabel yang memiliki pangkat tertinggi dari fungsi tersebut, oleh karena begin mathsize 14px style x rightwards arrow infinity end stylemaka ambilah nilai limitnya yang tidak mengandung variabel begin mathsize 14px style x end style seperti berikut ini:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses 9 x plus 3 close parentheses squared over open parentheses 3 x plus 8 close parentheses squared end cell equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 9 x plus 3 close parentheses open parentheses 9 x plus 3 close parentheses over denominator open parentheses 3 x plus 8 close parentheses open parentheses 3 x plus 8 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 81 x squared plus 54 x plus 9 over denominator 9 x squared plus 48 x plus 16 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 81 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 54 x over denominator x squared end fraction end style plus begin display style 9 over x squared end style over denominator begin display style fraction numerator 9 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 48 x over denominator x squared end fraction end style plus begin display style 16 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 81 plus 54 over x plus 9 over x squared end style over denominator begin display style 9 plus 48 over x plus 16 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 81 plus 0 plus 0 end style over denominator begin display style 9 plus 0 plus 0 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of 81 over 9 end cell row blank equals 9 row blank blank blank end table end style    

Dengan demikian nilai dari begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses 9 x plus 3 close parentheses squared over open parentheses 3 x plus 8 close parentheses squared equals 9 end style.

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