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Nilai x→3lim​ 2x−3​−x​x+2​−2x−1​​ adalah....

Pertanyaan

Nilai begin mathsize 14px style limit as x rightwards arrow 3 of space fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator square root of 2 x minus 3 end root minus square root of x end fraction end style adalah....undefined 

  1. begin mathsize 14px style negative 1 over 15 square root of 15 end style  

  2. size 14px minus size 14px 1 over size 14px 5 square root of size 14px 15 

  3. size 14px minus size 14px 1 over size 14px 3 square root of size 14px 15 

  4. begin mathsize 14px style 1 fifth square root of 15 end style 

  5. begin mathsize 14px style 1 over 15 square root of 15 end style 

T. Rizki

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Nilai limit pada soal di atas dapat dicari dengan cara mengalikannya dengan akar sekawan dari begin mathsize 14px style square root of 2 x minus 3 end root minus square root of x end style yaitu begin mathsize 14px style square root of 2 x minus 3 end root plus square root of x end style. Diperoleh   
 

begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator square root of 2 x minus 3 end root minus square root of x end fraction equals limit as x rightwards arrow 3 of open parentheses fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator square root of 2 x minus 3 end root minus square root of x end fraction times fraction numerator square root of 2 x minus 3 end root plus square root of x over denominator square root of 2 x minus 3 end root plus square root of x end fraction close parentheses equals limit as x rightwards arrow 3 of open parentheses fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator x minus 3 end fraction times square root of 2 x minus 3 end root plus square root of x close parentheses equals limit as x rightwards arrow 3 of fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator x minus 3 end fraction times limit as x rightwards arrow 3 of square root of 2 x minus 3 end root plus square root of x equals limit as x rightwards arrow 3 of fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator x minus 3 end fraction times 2 square root of 3 equals 2 square root of 3 open parentheses limit as x rightwards arrow 3 of fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator x minus 3 end fraction times fraction numerator square root of x plus 2 end root plus square root of 2 x minus 1 end root over denominator square root of x plus 2 end root plus square root of 2 x minus 1 end root end fraction close parentheses equals 2 square root of 3 open parentheses limit as x rightwards arrow 3 of fraction numerator negative x plus 3 over denominator x minus 3 end fraction times fraction numerator 1 over denominator square root of x plus 2 end root plus square root of 2 x minus 1 end root end fraction close parentheses equals negative 2 square root of 3 limit as x rightwards arrow 3 of fraction numerator 1 over denominator square root of x plus 2 end root plus square root of 2 x minus 1 end root end fraction equals negative 2 square root of 3 times fraction numerator 1 over denominator square root of 5 plus square root of 5 end fraction equals negative fraction numerator 2 square root of 3 over denominator 2 square root of 5 end fraction equals negative square root of 3 over 5 end root equals negative 1 fifth square root of 15 end style  

Jadi, jawaban yang tepat adalah B.

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