Roboguru

Nilai dari

Pertanyaan

Nilai dari limit as x rightwards arrow 1 of fraction numerator square root of 3 x plus 6 end root minus 3 over denominator 2 minus square root of 3 x plus 1 end root end fraction equals.... 

  1. 1 

  2. 1 half 

  3. fraction numerator negative 1 over denominator 3 end fraction 

  4. 3 over 2 

  5. fraction numerator negative 2 over denominator 3 end fraction 

Pembahasan Soal:

Dengan mengalikan akar sekawan.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of fraction numerator square root of 3 x plus 6 end root minus 3 over denominator 2 minus square root of 3 x plus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator square root of 3 x plus 6 end root minus 3 over denominator 2 minus square root of 3 x plus 1 end root end fraction times fraction numerator 2 plus square root of 3 x plus 1 end root over denominator 2 plus square root of 3 x plus 1 end root end fraction times fraction numerator square root of 3 x plus 6 end root plus 3 over denominator square root of 3 x plus 6 end root plus 3 end fraction space end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator open parentheses square root of 3 x plus 6 end root close parentheses squared minus 3 squared over denominator 2 squared minus open parentheses square root of 3 x plus 1 end root close parentheses squared end fraction times fraction numerator 2 plus square root of 3 x plus 1 end root over denominator square root of 3 x plus 6 end root plus 3 end fraction end cell row space equals cell limit as x rightwards arrow 1 of fraction numerator 3 x plus 6 minus 9 over denominator 4 minus open parentheses 3 x plus 1 close parentheses end fraction times fraction numerator 2 plus square root of 3 x plus 1 end root over denominator square root of 3 x plus 6 end root plus 3 end fraction space end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 3 x minus 3 over denominator 3 minus 3 x end fraction times fraction numerator 2 plus square root of 3 x plus 1 end root over denominator square root of 3 x plus 6 end root plus 3 end fraction space end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator negative up diagonal strike open parentheses 3 minus 3 x close parentheses end strike over denominator up diagonal strike open parentheses 3 minus 3 x close parentheses end strike end fraction times fraction numerator 2 plus square root of 3 x plus 1 end root over denominator square root of 3 x plus 6 end root plus 3 end fraction space end cell row blank equals cell limit as x rightwards arrow 1 of minus fraction numerator 2 plus square root of 3 x plus 1 end root over denominator square root of 3 x plus 6 end root plus 3 end fraction end cell row space equals cell negative fraction numerator 2 plus square root of 3 times 1 plus 1 end root over denominator square root of 3 times 1 plus 6 end root plus 3 end fraction end cell row space equals cell negative fraction numerator 2 plus square root of 4 over denominator square root of 9 plus 3 end fraction end cell row space equals cell negative fraction numerator 2 plus 2 over denominator 3 plus 3 end fraction space end cell row blank equals cell negative 4 over 6 space end cell row blank equals cell negative 2 over 3 end cell row blank equals cell fraction numerator negative 2 over denominator 3 end fraction end cell end table end style    

Jadi, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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