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Tentukan nilai dari: f.

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Tentukan nilai dari:

f. begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 8 x squared plus 2 x minus 1 over denominator 2 x plus 4 end fraction end style 

Pembahasan Video:

Pembahasan Soal:

Dengan menggunakan konsep limit tak hingga

Error converting from MathML to accessible text.

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 8 x squared plus 2 x minus 1 over denominator 2 x plus 4 end fraction end cell end tablemempunyai pangkat tertinggi pada pembilangnya 2 dan pangkat tertinggi pada penyebutnya 1, sehingga berdasarkan rumus diatas m greater than n maka :

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 8 x squared plus 2 x minus 1 over denominator 2 x plus 4 end fraction end cell equals infinity end table

Jadi, hasil limitnya adalah

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Kumaralalita

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 30 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

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 dan open parentheses a plus b close parentheses squared equals a squared plus 2 a b plus b squared

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator open parentheses 2 x plus 3 close parentheses squared minus 7 over denominator 8 x squared minus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 2 x close parentheses squared plus 2 times 2 x times 3 plus 3 squared minus 7 over denominator 8 x squared minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 4 x squared plus 12 x plus 2 over denominator 8 x squared minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 4 x squared plus 12 x plus 2 over denominator 8 x squared minus 1 end fraction cross 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 4 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 12 x over denominator x squared end fraction end style plus begin display style 2 over x squared end style over denominator begin display style fraction numerator 8 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 begin display style 4 plus 12 over x plus 2 over x squared end style over denominator begin display style 8 minus 1 over x squared end style end fraction end cell row blank equals cell fraction numerator 4 plus begin display style 12 over infinity end style plus begin display style 2 over infinity squared end style over denominator 8 minus begin display style 1 over infinity squared end style end fraction end cell row blank equals cell fraction numerator 4 plus 0 plus 0 over denominator 8 minus 0 end fraction end cell row blank equals cell 0 comma 5 end cell 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 open parentheses 2 x plus 3 close parentheses squared minus 7 over denominator 8 x squared minus 1 end fraction end cell end table equals 0 comma 5

Oleh karena itu, jawaban yang benar adalah C.

Roboguru

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 x squared left parenthesis x squared minus 2 x plus 1 right parenthesis over denominator x squared plus 4 x plus 5 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator x to the power of 4 minus 2 x cubed plus x squared over denominator x squared plus 4 x plus 5 end fraction 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 x rightwards arrow infinity of fraction numerator begin display style x to the power of 4 over x to the power of 4 end style minus begin display style fraction numerator 2 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 over denominator begin display style x squared over x to the power of 4 end style plus begin display style fraction numerator 4 x over denominator x to the power of 4 end fraction end style plus begin display style 5 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 1 minus 2 over x plus 1 over x squared end style over denominator begin display style 1 over x squared plus 4 over x cubed plus 5 over x to the power of 4 end style end fraction end cell row blank equals cell fraction numerator begin display style 1 minus 2 over infinity plus 1 over infinity squared end style over denominator begin display style 1 over infinity squared plus 4 over infinity cubed plus 5 over infinity to the power of 4 end style end fraction end cell row blank equals cell fraction numerator 1 minus 0 plus 0 over denominator 0 plus 0 plus 0 end fraction end cell row blank equals cell 1 over 0 end cell row blank equals infinity end table  

Dengan demikian, nilai dari limit di atas adalah begin mathsize 14px style infinity end style.

Jadi, jawaban yang tepat adalah E.

Roboguru

Nilai dari  adalah...

Pembahasan Soal:

Perhatikan penghitungan berikut! 

                          limit as x rightwards arrow infinity of space fraction numerator square root of 5 x plus 2020 end root minus square root of 4 x plus 2021 end root over denominator 4 x end fraction equals limit as x rightwards arrow infinity of space fraction numerator square root of begin display style fraction numerator 5 x over denominator x squared end fraction end style plus begin display style 2020 over x squared end style end root minus square root of begin display style fraction numerator 4 x over denominator x squared end fraction end style plus begin display style 2021 over x squared end style end root over denominator begin display style fraction numerator 4 x over denominator x end fraction end style end fraction equals limit as x rightwards arrow infinity of space fraction numerator square root of begin display style 5 over x plus 2020 over x squared end style end root minus square root of begin display style 4 over x plus 2021 over x squared end style end root over denominator begin display style 4 end style end fraction equals fraction numerator square root of begin display style 0 plus 0 end style end root minus square root of begin display style 0 plus 0 end style end root over denominator begin display style 4 end style end fraction equals 0 over 4 equals 0      

Jadi, nilai dari limit as x rightwards arrow infinity of space fraction numerator square root of 5 x plus 2020 end root minus square root of 4 x plus 2021 end root over denominator 4 x end fraction adalah 0. space 

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Pembahasan Soal:

Ingat kembali :

Error converting from MathML to accessible text.

limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 5 plus 3 x squared minus 5 x plus 7 over denominator 2 x to the power of 5 minus 8 x cubed plus 3 x minus 2 end fraction mempunyai pangkat tertinggi dari penyebut dan pembilangnya sama yaitu 5, sehingga berdasarkan rumus diatas :

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 5 plus 3 x squared minus 5 x plus 7 over denominator 2 x to the power of 5 minus 8 x cubed plus 3 x minus 2 end fraction end cell equals cell 4 over 2 end cell row blank equals 2 end table 

Jadi, nilai dari limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 5 plus 3 x squared minus 5 x plus 7 over denominator 2 x to the power of 5 minus 8 x cubed plus 3 x minus 2 end fraction adalah begin mathsize 14px style 2 end style

Roboguru

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 space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction cross 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 space fraction numerator square root of begin display style fraction numerator 3 x over denominator x squared end fraction end style minus begin display style 2 over x squared end style end root minus square root of begin display style fraction numerator 2 x over denominator x squared end fraction end style plus begin display style 4 over x squared end style end root over denominator begin display style x over x end style minus begin display style 6 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator square root of begin display style 3 over x minus 2 over x squared end style end root minus square root of begin display style 2 over x plus 4 over x squared end style end root over denominator begin display style 1 minus 6 over x end style end fraction end cell row blank equals cell fraction numerator square root of begin display style 3 over infinity minus 2 over infinity squared end style end root minus square root of begin display style 2 over infinity plus 4 over infinity squared end style end root over denominator begin display style 1 minus 6 over infinity end style end fraction end cell row blank equals cell space fraction numerator square root of begin display style 0 minus 0 end style end root minus square root of begin display style 0 plus 0 end style end root over denominator begin display style 1 minus 0 end style end fraction end cell row blank equals cell 0 over 1 end cell row blank equals 0 end table 

Jadi, hasil limitnya adalah 0.

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