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begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator open parentheses 4 x plus 2 close parentheses squared over denominator square root of 16 x to the power of 4 plus 1 end root end fraction equals... end style

Jawaban:

Cara menghitung limit tak hingga pada fungsi rasional yang memuat polinomial salah satunya adalah membagi setiap suku pada pembilang dan penyebut dengan pangkat tertinggi dari pembilang atau penyebut sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator open parentheses 4 x plus 2 close parentheses squared over denominator square root of 16 x to the power of 4 plus 1 end root end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 16 x squared plus 16 x plus 4 over denominator square root of 16 x to the power of 4 plus 1 end root end fraction cross times fraction numerator begin display style 1 over x squared end style over denominator begin display style 1 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 fraction numerator 16 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 16 x over denominator x squared end fraction end style plus begin display style 4 over x squared end style over denominator square root of begin display style fraction numerator 16 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style 1 over x to the power of 4 end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 16 plus begin display style 16 over x end style plus begin display style 4 over x squared end style over denominator square root of 16 plus begin display style 1 over x to the power of 4 end style end root end fraction end cell row blank equals cell fraction numerator 16 plus begin display style 16 over infinity end style plus begin display style 4 over infinity end style over denominator square root of 16 plus begin display style 1 over infinity end style end root end fraction end cell row blank equals cell fraction numerator 16 plus 0 plus 0 over denominator square root of 16 plus 0 end root end fraction end cell row blank equals cell 16 over 4 end cell row blank equals 4 end table end style

Dengan demikian hasilnya adalah begin mathsize 14px style 4 end style.

 

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