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Hitunglah nilai dari

Pertanyaan

Hitunglah nilai dari begin mathsize 14px style limit as x rightwards arrow 2 of invisible function application fraction numerator x minus 2 over denominator square root of 2 x plus 5 end root minus square root of 5 x minus 1 end root end fraction end style 

Pembahasan Video:

Pembahasan Soal:

Subtitusi nilai x:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator square root of 2 x plus 5 end root minus square root of 5 x minus 1 end root end fraction end cell equals cell fraction numerator 2 minus 2 over denominator square root of 2 times 2 plus 5 end root minus square root of 5 times 2 minus 1 end root end fraction end cell row blank equals cell 0 over 0 end cell end table end style

Karena hasilnya bentuk tak tentu 0 over 0, maka dlanjutkan dengan mengkalikan akar sekawan sebagi berikut:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator square root of 2 x plus 5 end root minus square root of 5 x minus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator x minus 2 over denominator square root of 2 x plus 5 end root minus square root of 5 x minus 1 end root end fraction times fraction numerator square root of 2 x plus 5 end root plus square root of 5 x minus 1 end root over denominator square root of 2 x plus 5 end root plus square root of 5 x minus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis square root of 2 x plus 5 end root plus square root of 5 x minus 1 end root right parenthesis over denominator left parenthesis 2 x plus 5 right parenthesis minus left parenthesis 5 x minus 1 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis square root of 2 x plus 5 end root plus square root of 5 x minus 1 end root right parenthesis over denominator 2 x plus 5 minus 5 x plus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis square root of 2 x plus 5 end root plus square root of 5 x minus 1 end root right parenthesis over denominator negative 3 x plus 6 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis square root of 2 x plus 5 end root plus square root of 5 x minus 1 end root right parenthesis over denominator negative 3 left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator square root of 2 x plus 5 end root plus square root of 5 x minus 1 end root over denominator negative 3 end fraction end cell row blank equals cell fraction numerator square root of 2 times 2 plus 5 end root plus square root of 5 times 2 minus 1 end root over denominator negative 3 end fraction end cell row blank equals cell fraction numerator 3 plus 3 over denominator negative 3 end fraction end cell row blank equals cell fraction numerator 6 over denominator negative 3 end fraction end cell row blank equals cell negative 2 end cell end table end style  

Jadi, begin mathsize 14px style 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 cell fraction numerator x minus 2 over denominator square root of 2 x plus 5 end root minus square root of 5 x minus 1 end root 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 minus end table 2 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 01 Agustus 2021

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