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Pertanyaan

limit as x rightwards arrow 4 of space fraction numerator x squared minus 16 over denominator square root of x minus square root of 3 square root of x minus 2 end root end fraction equals space...

  1. infinity 

  2. 108 

  3. 118 

  4. 0 

  5. 128 

Pembahasan Soal:

Berdasarkan konsep L'Hospital diperoleh hasil limit sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 4 of space fraction numerator x squared minus 16 over denominator square root of x minus square root of 3 square root of x minus 2 end root end fraction end cell row blank equals cell limit as x rightwards arrow 4 of space fraction numerator 2 x over denominator begin display style fraction numerator 1 over denominator 2 square root of x end fraction end style minus begin display style fraction numerator 1 over denominator 2 square root of 3 square root of x minus 2 end root end fraction end style times begin display style fraction numerator 3 over denominator 2 square root of x end fraction end style end fraction end cell row blank equals cell fraction numerator 2 times 4 over denominator fraction numerator 1 over denominator 2 square root of 4 end fraction minus fraction numerator 1 over denominator 2 square root of 3 square root of 4 minus 2 end root end fraction times fraction numerator 3 over denominator 2 square root of 4 end fraction end fraction end cell row blank equals cell fraction numerator 8 over denominator begin display style 1 fourth end style minus begin display style fraction numerator 1 over denominator 2 times square root of 4 end fraction end style times begin display style 3 over 4 end style end fraction end cell row blank equals cell fraction numerator 8 over denominator begin display style 1 fourth end style minus begin display style 3 over 16 end style end fraction end cell row blank equals cell fraction numerator 8 over denominator begin display style 1 over 16 end style end fraction end cell row blank equals cell 8 cross times 16 end cell row blank equals 128 end table

Oleh karena itu, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Juni 2021

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