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Nilai

Pertanyaan

Nilai begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator square root of x squared plus 7 end root minus square root of 4 x plus 4 end root over denominator x squared plus 2 x minus 15 end fraction equals.... end style 

  1. size 14px 1 over size 14px 6 

  2. size 14px 1 over size 14px 32 

  3. size 14px 16 

  4. size 14px 32 

  5. size 14px 64 

Pembahasan Video:

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator square root of x squared plus 7 end root minus square root of 4 x plus 4 end root over denominator x squared plus 2 x minus 15 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses square root of x squared plus 7 end root minus square root of 4 x plus 4 end root close parentheses open parentheses square root of x squared plus 7 end root plus square root of 4 x plus 4 end root close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 3 close parentheses open parentheses square root of x squared plus 7 end root plus square root of 4 x plus 4 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 3 close parentheses open parentheses x minus 1 close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 3 close parentheses open parentheses square root of x squared plus 7 end root plus square root of 4 x plus 4 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 1 close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses square root of x squared plus 7 end root plus square root of 4 x plus 4 end root close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 3 minus 1 close parentheses over denominator open parentheses 3 plus 5 close parentheses open parentheses square root of 9 plus 7 end root plus square root of 12 plus 4 end root close parentheses end fraction end cell row blank equals cell fraction numerator 2 over denominator 8 open parentheses 2 square root of 16 close parentheses end fraction end cell row blank equals cell 1 over 32 end cell row blank blank blank end table end style

Jadi, jawaban yang tepat adalah B.
 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Freelancer9

Terakhir diupdate 01 Mei 2021

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Pertanyaan yang serupa

Nilai  adalah ....

Pembahasan Soal:

Jika limit dari suatu fungsi tidak bisa ditentukan dengan substitusi langsung maka dapat ditentukan dengan cara pemfaktoran atau mengalikar akar sekawan. Misalnya diberikan fungsi fraction numerator square root of a x squared plus b end root plus c over denominator x minus d end fraction, maka fungsi tersebut dapat dikalikan dengan akar sekawan dari pembilangnya sebagai berikut. 

fraction numerator square root of a x squared plus b end root plus c over denominator x minus d end fraction times fraction numerator square root of a x squared plus b end root minus c over denominator square root of a x squared plus b end root minus c end fraction

Sehingga limit dari fungsi yang diminta pada soal di atas, dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of space fraction numerator square root of x squared plus 5 end root minus 3 over denominator x squared minus 2 x end fraction end cell equals cell limit as x rightwards arrow 2 of space fraction numerator square root of x squared plus 5 end root minus 3 over denominator x squared minus 2 x end fraction times fraction numerator square root of x squared plus 5 end root plus 3 over denominator square root of x squared plus 5 end root plus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator x squared plus 5 minus 9 over denominator open parentheses x squared minus 2 x close parentheses open parentheses square root of x squared plus 5 end root plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator x squared minus 4 over denominator x open parentheses x minus 2 close parentheses open parentheses square root of x squared plus 5 end root plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator x squared minus 2 squared over denominator x open parentheses x minus 2 close parentheses open parentheses square root of x squared plus 5 end root plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator open parentheses x plus 2 close parentheses up diagonal strike open parentheses x minus 2 close parentheses end strike over denominator x up diagonal strike open parentheses x minus 2 close parentheses end strike open parentheses square root of x squared plus 5 end root plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of space fraction numerator open parentheses x plus 2 close parentheses over denominator x open parentheses square root of x squared plus 5 end root plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 2 plus 2 close parentheses over denominator 2 open parentheses square root of 2 squared plus 5 end root plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 open parentheses square root of 9 plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 times 6 end fraction end cell row blank equals cell 1 third end cell end table 

Dengan demikian, nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of x squared plus 5 end root minus 3 over denominator x squared minus 2 x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third end cell end table.

0

Roboguru

Pembahasan Soal:

Dengan mengalikan akar sekawan, diperoleh perhitungan sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator 1 minus square root of x over denominator 1 minus x squared end fraction end cell equals cell limit as x rightwards arrow 1 of fraction numerator 1 minus square root of x over denominator 1 minus x squared end fraction cross times fraction numerator 1 plus square root of x over denominator 1 plus square root of x end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 1 minus x over denominator open parentheses 1 minus x squared close parentheses open parentheses 1 plus square root of x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator up diagonal strike 1 minus x end strike over denominator up diagonal strike left parenthesis 1 minus x right parenthesis end strike left parenthesis 1 plus x right parenthesis open parentheses 1 plus square root of x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 1 over denominator left parenthesis 1 plus x right parenthesis open parentheses 1 plus square root of x close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator left parenthesis 1 plus 1 right parenthesis left parenthesis 1 plus square root of 1 right parenthesis end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 times 2 end fraction end cell row blank equals cell 1 fourth end cell end table end style 

Jadi, diperoleh nilai begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 1 minus square root of x over denominator 1 minus x squared end fraction equals 1 fourth end style.

1

Roboguru

Nilai dari

Pembahasan Soal:

Langkah awal menentukan nilai limit adalah dengan mensubstitusi nilai x, maka

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction equals 0 over 0 end style

Setelah disubstitusi ternyata diperoleh bentuk tak tentu, sehingga untuk menyelesaikannya digunakan metode pemfaktoran

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction times fraction numerator 3 plus square root of 9 plus x end root over denominator 3 plus square root of 9 plus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 5 x times open parentheses 3 plus square root of 9 plus x end root close parentheses over denominator 9 minus left parenthesis 9 plus x right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 5 x times open parentheses 3 plus square root of 9 plus x end root close parentheses over denominator negative x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of minus 5 open parentheses 3 plus square root of 9 plus x end root close parentheses end cell row blank equals cell negative 5 open parentheses 3 plus square root of 9 plus 0 end root close parentheses end cell row blank equals cell negative 30 end cell end table end style

Jadi, diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 5 x over denominator 3 minus square root of 9 plus x end root end fraction end cell end table equals negative 30 end style.

0

Roboguru

Nilai  adalah ....

Pembahasan Soal:

Dengan menerapkan konsep perkalian sekawan;

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 4 of fraction numerator straight x squared minus 16 over denominator 1 minus square root of straight x minus 3 end root end fraction end cell equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis over denominator 1 minus square root of straight x minus 3 end root end fraction times fraction numerator left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator left parenthesis 1 squared minus left parenthesis square root of straight x minus 3 end root right parenthesis squared end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator 1 minus left parenthesis straight x minus 3 right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator 1 minus straight x plus 3 end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x squared minus 16 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator 4 minus straight x end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x minus 4 right parenthesis left parenthesis straight x plus 4 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator negative left parenthesis straight x minus 4 right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x plus 4 right parenthesis left parenthesis 1 plus square root of straight x minus 3 end root right parenthesis over denominator negative 1 end fraction end cell row blank equals cell fraction numerator left parenthesis 4 plus 4 right parenthesis left parenthesis 1 plus square root of 4 minus 3 end root right parenthesis over denominator negative 1 end fraction end cell row blank equals cell fraction numerator 8 times 2 over denominator negative 1 end fraction end cell row blank equals cell negative 16 end cell end table end style  

Jadi, Nilai dari undefined.

Oleh karena itu, Jawaban yang benar adalah A

0

Roboguru

Hitunglah nilai limit fungsi berikut:

Pembahasan Soal:

limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 x minus 3 square root of x plus 1 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator open parentheses x minus 1 close parentheses squared end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 x minus 3 square root of x plus 1 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator open parentheses x minus 1 close parentheses open parentheses x minus 1 close parentheses end fraction times fraction numerator square root of x plus 1 over denominator square root of x plus 1 end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator open parentheses 2 square root of x minus 1 close parentheses open parentheses square root of x minus 1 close parentheses left parenthesis x minus 1 right parenthesis over denominator left parenthesis x minus 1 right parenthesis open parentheses x minus 1 close parentheses open parentheses square root of x plus 1 close parentheses end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 square root of x minus 1 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator open parentheses x minus 1 close parentheses open parentheses square root of x plus 1 close parentheses end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 square root of x minus 1 right parenthesis left parenthesis square root of x minus 1 right parenthesis over denominator open parentheses square root of x minus 1 close parentheses open parentheses square root of x plus 1 close parentheses open parentheses square root of x plus 1 close parentheses end fraction left right double arrow limit as x rightwards arrow 1 of fraction numerator left parenthesis 2 square root of x minus 1 right parenthesis over denominator open parentheses square root of x plus 1 close parentheses open parentheses square root of x plus 1 close parentheses end fraction equals 1 fourth 

0

Roboguru

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