Roboguru

x→∞lim​5x2+7x−12x2−3x+4​=....

Pertanyaan

limit as x rightwards arrow infinity of fraction numerator 2 x squared minus 3 x plus 4 over denominator 5 x squared plus 7 x minus 1 end fraction equals....

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

Hasil dari x→∞lim​(3x+8)2(9x+3)2​ adalah ...

Pembahasan Soal:

Dengan menggunakan konsep limit tak hingga, uraikan terlebih dahulu bentuk aljabar tersebut, kemudian bagi semua suku dengan variabel yang memiliki pangkat tertinggi dari fungsi tersebut, oleh karena begin mathsize 14px style x rightwards arrow infinity end stylemaka ambilah nilai limitnya yang tidak mengandung variabel begin mathsize 14px style x end style seperti berikut ini:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses 9 x plus 3 close parentheses squared over open parentheses 3 x plus 8 close parentheses squared end cell equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 9 x plus 3 close parentheses open parentheses 9 x plus 3 close parentheses over denominator open parentheses 3 x plus 8 close parentheses open parentheses 3 x plus 8 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 81 x squared plus 54 x plus 9 over denominator 9 x squared plus 48 x plus 16 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 81 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 54 x over denominator x squared end fraction end style plus begin display style 9 over x squared end style over denominator begin display style fraction numerator 9 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 48 x over denominator x squared end fraction end style plus begin display style 16 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 81 plus 54 over x plus 9 over x squared end style over denominator begin display style 9 plus 48 over x plus 16 over x squared end style end fraction end cell row blank equals cell fraction numerator begin display style 81 plus 0 plus 0 end style over denominator begin display style 9 plus 0 plus 0 end style end fraction end cell row blank equals cell 81 over 9 end cell row blank equals 9 row blank blank blank end table    

Dengan demikian nilai dari begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses 9 x plus 3 close parentheses squared over open parentheses 3 x plus 8 close parentheses squared equals 9 end style.

0

Roboguru

Hasil dari x→∞lim​⎝⎛​3+3+3+x3​3​3​⎠⎞​ adalah....

Pembahasan Soal:

Dengan menggunakan konsep limit menuju tak hingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses 3 plus fraction numerator 3 over denominator 3 plus begin display style fraction numerator 3 over denominator 3 plus begin display style 3 over x end style end fraction end style end fraction close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses 3 plus fraction numerator 3 over denominator 3 plus begin display style fraction numerator 3 over denominator begin display style fraction numerator 3 x plus 3 over denominator x end fraction end style end fraction end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses 3 plus fraction numerator 3 over denominator 3 plus begin display style fraction numerator 3 x over denominator begin display style 3 x plus 3 end style end fraction end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses 3 plus fraction numerator 3 over denominator begin display style fraction numerator 9 x plus 9 plus 3 x over denominator begin display style 3 x plus 3 end style end fraction end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses 3 plus fraction numerator 3 over denominator begin display style fraction numerator 12 x plus 9 over denominator begin display style 3 x plus 3 end style end fraction end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses 3 plus fraction numerator 3 open parentheses 3 x plus 3 close parentheses over denominator begin display style 12 x plus 9 end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses 3 plus fraction numerator 9 x plus 9 over denominator begin display style 12 x plus 9 end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses 3 plus fraction numerator 9 x plus 9 over denominator begin display style 12 x plus 9 end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses fraction numerator 36 x plus 27 plus 9 x plus 9 over denominator begin display style 12 x plus 9 end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses fraction numerator 45 x plus 36 over denominator begin display style 12 x plus 9 end style end fraction close parentheses times fraction numerator begin display style 1 over x end style over denominator begin display style 1 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses fraction numerator begin display style fraction numerator 45 x over denominator x end fraction end style plus begin display style 36 over x end style over denominator begin display style fraction numerator begin display style 12 x end style over denominator x end fraction plus fraction numerator begin display style 9 end style over denominator x end fraction end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses fraction numerator begin display style 45 plus 36 over x end style over denominator begin display style 12 plus fraction numerator begin display style 9 end style over denominator x end fraction end style end fraction close parentheses end cell end table 

ingat bahwa limit as x rightwards arrow infinity of a over x to the power of n equals 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses fraction numerator begin display style 45 plus 36 over x end style over denominator begin display style 12 plus fraction numerator begin display style 9 end style over denominator x end fraction end style end fraction close parentheses end cell equals cell fraction numerator 45 plus 0 over denominator 12 plus 0 end fraction end cell row blank equals cell 45 over 12 end cell row blank equals cell 15 over 4 end cell end table 

Dengan demikian hasil dari limit as x rightwards arrow infinity of open parentheses 3 plus fraction numerator 3 over denominator 3 plus begin display style fraction numerator 3 over denominator 3 plus begin display style 3 over x end style end fraction end style end fraction close parentheses equals 15 over 4.

0

Roboguru

x→∞lim​2x2x2−5​−1​= ...

Pembahasan Soal:

0

Roboguru

x→∞lim​2x4+x−16x5−7x2+1​=....

Pembahasan Soal:

Bagi setiap suku dengan variabel pangkat tertinggi pada penyebut

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator 6 x to the power of 5 minus 7 x squared plus 1 over denominator 2 x to the power of 4 plus x minus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 6 x to the power of 5 over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 7 x squared 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 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 x over x to the power of 4 end style minus begin display style 1 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 6 x minus 7 over x squared plus 1 over x to the power of 4 end style over denominator begin display style 2 plus 1 over x cubed minus 1 over x to the power of 4 end style end fraction end cell row blank blank blank end table 

Ingat bahwa limit as x rightwards arrow infinity of a over x to the power of n equals 0 sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator begin display style 6 x minus 7 over x squared plus 1 over x to the power of 4 end style over denominator begin display style 2 plus 1 over x cubed minus 1 over x to the power of 4 end style end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 6 x minus 0 plus 0 over denominator 2 plus 0 minus 0 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 6 x over denominator 2 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space 3 x end cell row blank equals cell 3 times infinity end cell row blank equals infinity end table  

Jadi, jawaban yang tepat adalah E.

0

Roboguru

x→∞lim​6x4−7x+92x3+6x2+7x−5​=…

Pembahasan Soal:

Konsep limit  tak hingga fungsi rasional adalah dengan metode membagi dengan pangkat tertinggi

Diketahui: table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator 2 x cubed plus 6 x squared plus 7 x minus 5 over denominator 6 x to the power of 4 minus 7 x plus 9 end fraction end cell end table

Pangkat tertinggi adalah x to the power of 4, maka pembilang dan penyebut dibagi oleh x to the power of 4, maka diperoleh penyelesaiannya sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 2 x cubed plus 6 x squared plus 7 x minus 5 over denominator 6 x to the power of 4 minus 7 x plus 9 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 x cubed over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 6 x squared over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 7 x over denominator x to the power of 4 end fraction end style minus begin display style 5 over x to the power of 4 end style over denominator begin display style fraction numerator 6 x to the power of 4 over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 7 x over denominator x to the power of 4 end fraction end style plus begin display style 9 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 over x plus 6 over x squared plus 7 over x cubed minus 5 over x to the power of 4 end style over denominator begin display style 6 minus 7 over x cubed plus 9 over x to the power of 4 end style end fraction end cell row blank equals cell fraction numerator 0 plus 0 plus 0 minus 0 over denominator 6 minus 0 plus 0 end fraction end cell row blank equals cell 0 over 6 end cell row blank equals 0 end table

 

Jadi, nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator 2 x cubed plus 6 x squared plus 7 x minus 5 over denominator 6 x to the power of 4 minus 7 x plus 9 end fraction end cell end table adalah 0.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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