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Pertanyaan

 begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator square root of 2 x plus 1 end root minus square root of x plus 5 end root over denominator 4 minus x end fraction equals... end style    

 

 

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

hasil dari table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator square root of 2 x plus 1 end root minus square root of x plus 5 end root over denominator 4 minus x end fraction end cell equals cell negative 1 over 6 end cell end table 

Pembahasan

Cara utama dalam menentukan nilai limit adalah dengan menggunakan metode substitusi. Apabila hasil substitusi tersebut merupakan bentuk tak tentu, selanjutnya penyelesaian harus menggunakan cara lain, yaitu metode pemfaktoran atau kali akar sekawan.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator square root of 2 x plus 1 end root minus square root of x plus 5 end root over denominator 4 minus x end fraction end cell equals cell fraction numerator square root of 2 times 4 plus 1 end root minus square root of 4 plus 5 end root over denominator 4 minus 4 end fraction end cell row blank equals cell fraction numerator 3 minus 3 over denominator 0 end fraction end cell row blank equals cell 0 over 0 end cell end table

Hasil dari substitusi merupakan bentuk tak tentu sehingga penyelesaian limit tersebut menggunakan perkalian akar sekawan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 4 of fraction numerator square root of 2 x plus 1 end root minus square root of x plus 5 end root over denominator 4 minus x end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator square root of 2 x plus 1 end root minus square root of x plus 5 end root over denominator 4 minus x end fraction cross times fraction numerator square root of 2 x plus 1 end root plus square root of x plus 5 end root over denominator square root of 2 x plus 1 end root plus square root of x plus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator 2 x plus 1 minus left parenthesis x plus 5 right parenthesis over denominator open parentheses 4 minus x close parentheses open parentheses square root of 2 x plus 1 end root plus square root of x plus 5 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator x minus 4 over denominator open parentheses 4 minus x close parentheses left parenthesis square root of 2 x plus 1 end root plus square root of x plus 5 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator negative 1 over denominator left parenthesis square root of 2 x plus 1 end root plus square root of x plus 5 end root right parenthesis end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 3 plus 3 end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 6 end fraction end cell end table end style 

Dengan demikian, hasil dari table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator square root of 2 x plus 1 end root minus square root of x plus 5 end root over denominator 4 minus x end fraction end cell equals cell negative 1 over 6 end cell end table 

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