Roboguru

Hitunglah nilai dari .

Pertanyaan

Hitunglah nilai dari begin mathsize 14px style 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 style.

Pembahasan Soal:

Menggunakan konsep penyelesaian limit dengan mengalikan sekawannya, 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 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 row blank 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 open parentheses square root of 2 plus x end root plus square root of 2 minus x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 x over denominator x open parentheses square root of 2 plus x end root plus square root of 2 minus x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 over denominator open parentheses square root of 2 plus x end root plus square root of 2 minus x end root close parentheses end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 2 plus square root of 2 end fraction end cell row blank equals cell fraction numerator 2 over denominator 2 square root of 2 end fraction equals fraction numerator 1 over denominator square root of 2 end fraction equals 1 half square root of 2 end cell end table end style 

Jadi, nilai dari limit tersebut adalah begin mathsize 14px style bottom enclose bold 1 over bold 2 square root of bold 2 end enclose end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Maret 2021

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