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Hitunglah limit fungsi berikut. x → ∞ lim ​ 2 x 3 + x − 1 3 x 2 − 5 ​

Hitunglah limit fungsi berikut.

         

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N. Puspita

Master Teacher

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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x squared minus 5 over denominator 2 x cubed plus x minus 1 end fraction end cell end table equals 0.

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Ingat: . Jadi .

Ingat: limit as x rightwards arrow infinity of k over x to the power of n equals k over infinity to the power of n equals 0.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 3 x squared minus 5 over denominator 2 x cubed plus x minus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 3 x squared minus 5 over denominator 2 x cubed plus x minus 1 end fraction cross times fraction numerator begin display style 1 over x cubed end style over denominator begin display style 1 over x cubed end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 3 x squared over denominator x cubed end fraction end style minus begin display style 5 over x cubed end style over denominator begin display style fraction numerator 2 x cubed over denominator x cubed end fraction end style plus begin display style x over x cubed end style minus begin display style 1 over x cubed end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 3 over x end style minus begin display style 5 over x cubed end style over denominator 2 plus begin display style 1 over x squared end style minus begin display style 1 over x cubed end style end fraction end cell row blank equals cell fraction numerator begin display style 3 over infinity minus 5 over infinity cubed end style over denominator 2 plus begin display style 1 over infinity squared end style minus begin display style 1 over infinity cubed end style end fraction end cell row blank equals cell fraction numerator 0 minus 0 over denominator 2 plus 0 minus 0 end fraction end cell row blank equals cell 0 over 2 end cell row blank equals 0 end table

Jadi table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x squared minus 5 over denominator 2 x cubed plus x minus 1 end fraction end cell end table equals 0.

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