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Tentukan nilai dari

Pertanyaan

Tentukan nilai dari begin mathsize 14px style limit as x rightwards arrow 0 of invisible function application fraction numerator square root of 2 plus x end root minus square root of 2 minus x end root over denominator x end fraction end style 

Pembahasan Video:

Pembahasan Soal:

Subtitusi nilai x:

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 square root of 2 plus x end root minus square root of 2 minus x end root over denominator x end fraction end cell equals cell fraction numerator square root of 2 plus 0 end root minus square root of 2 minus 0 end root over denominator 0 end fraction end cell row blank equals cell 0 over 0 end cell row blank blank blank end table end style

Karena hasil tidak terdefinisi, maka difaktorkan sebagai berikut:

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

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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