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Nilai dari x→∞lim​(x+2)(x−3)3x4−2x2+x​ adalah ....

Pertanyaan

Nilai dari begin mathsize 14px style limit as straight x rightwards arrow infinity of fraction numerator 3 straight x to the power of 4 minus 2 straight x squared plus straight x over denominator left parenthesis straight x plus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction end style adalah ....

Pembahasan Soal:

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 straight x rightwards arrow infinity of fraction numerator 3 straight x to the power of 4 minus 2 straight x squared plus straight x over denominator left parenthesis straight x plus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction end cell equals cell limit as straight x rightwards arrow infinity of fraction numerator 3 straight x to the power of 4 minus 2 straight x squared plus straight x over denominator straight x squared minus straight x minus 6 end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator 3 straight x to the power of 4 minus 2 straight x squared plus straight x over denominator straight x squared minus straight x minus 6 end fraction cross times fraction numerator begin display style 1 over x to the power of 4 end style over denominator begin display style 1 over x to the power of 4 end style end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style fraction numerator 3 straight x to the power of 4 over denominator straight x to the power of 4 end fraction minus fraction numerator 2 straight x squared over denominator straight x to the power of 4 end fraction plus straight x over straight x to the power of 4 end style over denominator begin display style straight x squared over straight x to the power of 4 minus straight x over straight x to the power of 4 minus 6 over straight x to the power of 4 end style end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style 3 minus 2 over straight x squared plus 1 over straight x cubed end style over denominator begin display style 1 over straight x squared minus 1 over straight x cubed minus 6 over straight x to the power of 4 end style end fraction space end cell row blank equals cell fraction numerator begin display style 3 minus 2 over infinity squared plus 1 over infinity cubed end style over denominator begin display style 1 over infinity squared minus 1 over infinity cubed minus 6 over infinity to the power of 4 end style end fraction end cell row blank equals cell fraction numerator begin display style 3 minus 0 plus 0 end style over denominator begin display style 0 minus 0 minus 0 end style end fraction end cell row blank equals cell fraction numerator begin display style 3 end style over denominator begin display style 0 end style end fraction end cell row blank equals infinity end table  

Jadi, Nilai dari begin mathsize 14px style limit as straight x rightwards arrow infinity of fraction numerator 3 straight x to the power of 4 minus 2 straight x squared plus straight x over denominator left parenthesis straight x plus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction end style adalah begin mathsize 14px style infinity end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 07 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

x→∞lim​6x5−2x3+8x22x5+x4−7x3​=....

Pembahasan Soal:

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 2 x to the power of 5 plus x to the power of 4 minus 7 x cubed over denominator 6 x to the power of 5 minus 2 x cubed plus 8 x squared end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 2 x to the power of 5 plus x to the power of 4 minus 7 x cubed over denominator 6 x to the power of 5 minus 2 x cubed plus 8 x squared end fraction cross times fraction numerator begin display style 1 over x to the power of 5 end style over denominator begin display style 1 over x to the power of 5 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 x to the power of 5 over denominator x to the power of 5 end fraction end style plus begin display style x to the power of 4 over x to the power of 5 end style minus begin display style fraction numerator 7 x cubed over denominator x to the power of 5 end fraction end style over denominator begin display style fraction numerator 6 x to the power of 5 over denominator x to the power of 5 end fraction end style minus begin display style fraction numerator 2 x cubed over denominator x to the power of 5 end fraction end style plus begin display style fraction numerator 8 x squared over denominator x to the power of 5 end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 2 plus begin display style 1 over x end style minus begin display style 7 over x squared end style over denominator 6 minus begin display style 2 over x squared end style plus begin display style 8 over x cubed end style end fraction end cell row blank equals cell fraction numerator 2 plus begin display style 1 over infinity end style minus begin display style 7 over infinity squared end style over denominator 6 minus begin display style 2 over infinity squared end style plus begin display style 8 over infinity cubed end style end fraction end cell row blank equals cell fraction numerator 2 plus 0 minus 0 over denominator 6 minus 0 plus 0 end fraction end cell row blank equals cell 2 over 6 end cell row blank equals cell 1 third end cell end table

Jadi limit as x rightwards arrow infinity of fraction numerator 2 x to the power of 5 plus x to the power of 4 minus 7 x cubed over denominator 6 x to the power of 5 minus 2 x cubed plus 8 x squared end fraction equals 1 third. 

0

Roboguru

x→∞lim​(2x+5)2(4x−3)2​=....

Pembahasan Soal:

Ingat bahwa

limit as x rightwards arrow infinity of 1 over x to the power of n equals 0 comma space n greater than 0

Maka dapat diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses 4 x minus 3 close parentheses squared over open parentheses 2 x plus 5 close parentheses squared end cell equals cell limit as x rightwards arrow infinity of fraction numerator 16 x squared minus 24 x plus 9 over denominator 4 x squared plus 20 x plus 25 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x squared open parentheses 16 minus begin display style 24 over x end style plus begin display style 9 over x squared end style close parentheses over denominator x squared open parentheses 4 plus begin display style 20 over x end style plus begin display style 25 over x squared end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 16 minus begin display style 24 over x end style plus begin display style 9 over x squared end style over denominator 4 plus begin display style 20 over x end style plus begin display style 25 over x squared end style end fraction end cell row blank equals cell fraction numerator 16 minus 0 plus 0 over denominator 4 plus 0 plus 0 end fraction end cell row blank equals 4 end table

Jadi, limit as x rightwards arrow infinity of open parentheses 4 x minus 3 close parentheses squared over open parentheses 2 x plus 5 close parentheses squared equals 4 

0

Roboguru

x→∞lim​2x5+3x3−2x−1(x−2)2(x3+5)​

Pembahasan Soal:

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

limit as x rightwards arrow infinity of fraction numerator left parenthesis x minus 2 right parenthesis squared left parenthesis x cubed plus 5 right parenthesis over denominator 2 x to the power of 5 plus 3 x cubed minus 2 x minus 1 end fraction equals limit as x rightwards arrow infinity of fraction numerator left parenthesis x squared minus 4 x plus 4 right parenthesis left parenthesis x cubed plus 5 right parenthesis over denominator 2 x to the power of 5 plus 3 x cubed minus 2 x minus 1 end fraction equals limit as x rightwards arrow infinity of fraction numerator x to the power of 5 plus 5 x squared minus 4 x to the power of 4 minus 20 x plus 4 x cubed plus 20 over denominator 2 x to the power of 5 plus 3 x cubed minus 2 x minus 1 end fraction cross times fraction numerator begin display style 1 over x to the power of 5 end style over denominator begin display style 1 over x to the power of 5 end style end fraction equals limit as x rightwards arrow infinity of fraction numerator begin display style x to the power of 5 over x to the power of 5 minus fraction numerator 4 x to the power of 4 over denominator x to the power of 5 end fraction plus fraction numerator 4 x cubed over denominator x to the power of 5 end fraction end style plus begin display style fraction numerator 5 x squared over denominator x to the power of 5 end fraction end style minus begin display style fraction numerator 20 x over denominator x to the power of 5 end fraction end style plus begin display style 20 over x to the power of 5 end style over denominator begin display style fraction numerator 2 x to the power of 5 over denominator x to the power of 5 end fraction end style plus begin display style fraction numerator 3 x cubed over denominator x to the power of 5 end fraction end style minus begin display style fraction numerator 2 x over denominator x to the power of 5 end fraction end style minus begin display style 1 over x to the power of 5 end style end fraction equals limit as x rightwards arrow infinity of fraction numerator begin display style 1 minus 4 over x plus 4 over x squared plus 5 over x cubed minus 20 over x to the power of 4 plus 20 over x to the power of 5 end style over denominator begin display style 2 plus 3 over x squared minus 2 over x to the power of 4 minus 1 over x to the power of 5 end style end fraction equals fraction numerator begin display style 1 minus 4 over infinity plus 4 over infinity squared plus 5 over infinity cubed minus 20 over infinity to the power of 4 plus 20 over infinity to the power of 5 end style over denominator begin display style 2 plus 3 over infinity squared minus 2 over infinity to the power of 4 minus 1 over infinity to the power of 5 end style end fraction equals fraction numerator 1 plus begin display style 0 end style minus begin display style 0 end style minus 0 plus begin display style 0 end style plus begin display style 0 end style over denominator 2 plus begin display style 0 end style minus begin display style 0 end style minus begin display style 0 end style end fraction equals 1 half

Jadi limit as x rightwards arrow infinity of fraction numerator left parenthesis x minus 2 right parenthesis squared left parenthesis x cubed plus 5 right parenthesis over denominator 2 x to the power of 5 plus 3 x cubed minus 2 x minus 1 end fraction equals 1 half 

1

Roboguru

Hitunglah! x→∞lim​2x−1x2​−2x+1x2​=...

Pembahasan Soal:

Perhatikan penghitungan berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator x squared over denominator 2 x minus 1 end fraction minus fraction numerator x squared over denominator 2 x plus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator left parenthesis 2 x plus 1 right parenthesis x squared minus left parenthesis 2 x minus 1 right parenthesis x squared over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis 2 x plus 1 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 2 x cubed plus x squared minus 2 x cubed plus x squared over denominator 4 x squared plus 2 x minus 2 x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 2 x squared over denominator 4 x squared minus 1 end fraction 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 2 x squared over denominator x squared end fraction end style over denominator begin display style fraction numerator 4 x squared over denominator x squared end fraction end style minus 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 2 over denominator 4 minus 1 over x squared end fraction end cell row blank equals cell fraction numerator 2 over denominator 4 minus 1 over infinity end fraction end cell row blank equals cell fraction numerator 2 over denominator 4 minus 0 end fraction end cell row blank equals cell 2 over 4 end cell row blank equals cell 1 half end cell row blank blank blank end table

Jadi, hasil dari limit as x rightwards arrow infinity of fraction numerator x squared over denominator 2 x minus 1 end fraction minus fraction numerator x squared over denominator 2 x plus 1 end fraction adalah 1 half. 

2

Roboguru

x→∞lim​4x−2x2−5x33x3−2x−10​=…

Pembahasan Soal:

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 cubed minus 2 x minus 10 over denominator 4 x minus 2 x squared minus 5 x cubed end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 3 x cubed minus 2 x minus 10 over denominator 4 x minus 2 x squared minus 5 x cubed end fraction 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 cubed over denominator x cubed end fraction end style minus begin display style fraction numerator 2 x over denominator x cubed end fraction end style minus begin display style 10 over x cubed end style over denominator begin display style fraction numerator 4 x over denominator x cubed end fraction end style minus begin display style fraction numerator 2 x squared over denominator x cubed end fraction end style minus begin display style fraction numerator 5 x cubed over denominator x cubed end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 3 minus 2 over x squared minus 10 over x cubed end style over denominator begin display style 4 over x squared minus 2 over x minus 5 end style end fraction end cell row blank equals cell fraction numerator begin display style 3 minus 2 over infinity squared minus 10 over infinity cubed end style over denominator begin display style 4 over infinity squared minus 2 over infinity minus 5 end style end fraction end cell row blank equals cell fraction numerator 3 minus 0 minus 0 over denominator 0 minus 0 minus 5 end fraction end cell row blank equals cell negative 3 over 5 end cell end table 

Dengan demikian, nilai dari limit di atas adalah size 14px minus size 14px 3 over size 14px 5.

Jadi, jawaban yang tepat adalah A.

1

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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