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begin mathsize 14px style limit as x rightwards arrow 1 of invisible function application fraction numerator square root of x minus square root of 2 x minus 1 end root over denominator x minus 1 end fraction equals horizontal ellipsis end style 

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Pembahasan Soal:

Jika dijumpai limit dengan bentuk akar dan tidak dapat difaktorkan secara langsung, maka kalikan dengan bentuk sekawannya.

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

Jadi nilai begin mathsize 14px style limit as x rightwards arrow 1 of invisible function application fraction numerator square root of x minus square root of 2 x minus 1 end root over denominator x minus 1 end fraction equals negative 1 half end style.

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Terakhir diupdate 12 April 2021

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