Nilai x→0lim​x4+2x​−4−2x​​=...

Pertanyaan

Nilai begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of 4 plus 2 x end root minus square root of 4 minus 2 x end root over denominator x end fraction equals... end style 

  1. begin mathsize 14px style 4 end style 

  2. begin mathsize 14px style 2 end style 

  3. begin mathsize 14px style 1 end style 

  4. begin mathsize 14px style 0 end style 

  5. begin mathsize 14px style negative 1 end style 

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C. 

Pembahasan

Pada soal limit tersebut terdapat bentuk akar, sehingga untuk menentukan nilai limit tersebut dengan mengalikan dengan akar sekawan.

Apabila begin mathsize 14px style x equals 0 end style akan diperoleh bentuk begin mathsize 14px style 0 over 0 end style, atau bentuk tak tentu suatu limit, sehingga bentuk limit tersebut harus dikalikan dengan akar sekawannya, seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator square root of 4 plus 2 x end root minus square root of 4 minus 2 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 4 plus 2 x end root minus square root of 4 minus 2 x end root over denominator x end fraction cross times fraction numerator square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root over denominator square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses 4 plus 2 x close parentheses minus open parentheses 4 minus 2 x close parentheses over denominator x open parentheses square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 4 plus 2 x minus 4 plus 2 x over denominator x open parentheses square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 4 x over denominator x open parentheses square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 4 over denominator open parentheses square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root close parentheses end fraction end cell row blank equals cell fraction numerator 4 over denominator open parentheses square root of 4 plus 2 open parentheses 0 close parentheses end root plus square root of 4 minus 2 open parentheses 0 close parentheses end root close parentheses end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 4 plus square root of 4 end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 plus 2 end fraction end cell row blank equals cell 4 over 4 end cell row blank equals 1 end table end style 

Sehingga diperoleh begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of 4 plus 2 x end root minus square root of 4 minus 2 x end root over denominator x end fraction equals 1 end style.

Jadi, jawaban yang tepat adalah C. 

101

4.3 (8 rating)

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