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Hitunglah nilai limit fungsi berikut.

Hitunglah nilai limit fungsi berikut.

begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 2 x to the power of 4 minus 3 x squared plus 3 over denominator 3 x to the power of 4 plus 2 x cubed minus 5 x squared plus 7 end fraction end style 

Jawaban:

Dengan menggunakan konsep limit tak hingga, bagilah semua suku dengan variabel yang memiliki pangkat tertinggi dari fungsi tersebut, oleh karena begin mathsize 14px style x rightwards arrow infinity end style maka 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 fraction numerator 2 x to the power of 4 minus 3 x squared plus 3 over denominator 3 x to the power of 4 plus 2 x cubed minus 5 x squared plus 7 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 x to the power of 4 over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 3 x squared over denominator x to the power of 4 end fraction end style plus begin display style 3 over x to the power of 4 end style over denominator begin display style fraction numerator 3 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 2 x cubed over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 5 x squared over denominator x to the power of 4 end fraction end style plus begin display style 7 over x to the power of 4 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 minus 3 over x squared plus 3 over x to the power of 4 end style over denominator begin display style 3 plus 2 over x minus 5 over x squared plus 7 over x to the power of 4 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 minus 0 plus 0 end style over denominator begin display style 3 plus 0 minus 0 plus 0 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 end style over denominator begin display style 3 end style end fraction end cell row blank equals cell 2 over 3 end cell end table end style     

Dengan demikian nilai dari limit fungsi tersebut adalah begin mathsize 14px style 2 over 3 end style.

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