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Pertanyaan

begin mathsize 14px style limit as x rightwards arrow infinity of space fraction numerator 4 x cubed plus x squared plus 1 over denominator 2 x to the power of 4 plus 3 end fraction equals... end style 

Pembahasan Soal:

Gunakan konsep limit tak hingga. 

Perhatikan perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator 4 x cubed plus x squared plus 1 over denominator 2 x to the power of 4 plus 3 end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 4 x cubed over denominator x to the power of 4 end fraction end style plus begin display style x squared over x to the power of 4 end style plus begin display style 1 over x to the power of 4 end style over denominator begin display style fraction numerator 2 x to the power of 4 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 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style 4 over x end style plus begin display style 1 over x squared end style plus begin display style 1 over x to the power of 4 end style over denominator 2 plus begin display style 3 over x to the power of 4 end style end fraction end cell row blank equals cell fraction numerator 0 plus 0 plus 0 over denominator 2 plus 0 end fraction end cell row blank equals cell 0 over 2 end cell row cell limit as x rightwards arrow infinity of space fraction numerator 4 x cubed plus x squared plus 1 over denominator 2 x to the power of 4 plus 3 end fraction end cell equals 0 end table end style 

Jadi, diperoleh begin mathsize 14px style limit as x rightwards arrow infinity of space fraction numerator 4 x cubed plus x squared plus 1 over denominator 2 x to the power of 4 plus 3 end fraction equals 0 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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