nilai dari x→3lim​ 1−x2x−2​−3x​​=...

Pertanyaan

nilai dari begin mathsize 14px style limit as x rightwards arrow 3 of space fraction numerator square root of 2 x minus 2 end root minus square root of 3 x end root over denominator 1 minus x end fraction equals end style...

  1. begin mathsize 14px style 2 end style 

  2. begin mathsize 14px style 0 end style 

  3. begin mathsize 14px style 1 half end style 

  4. begin mathsize 14px style negative 1 half end style 

  5. begin mathsize 14px style negative 2 end style 

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Dengan menggunakan metode substitusi pada limit fungsi, maka substitusikan begin mathsize 14px style x equals 3 end style sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator square root of 2 x minus 2 end root minus square root of 3 x end root over denominator 1 minus x end fraction end cell equals cell fraction numerator square root of 2 open parentheses 3 close parentheses minus 2 end root minus square root of 3 open parentheses 3 close parentheses end root over denominator 1 minus 3 end fraction end cell row blank equals cell fraction numerator square root of 6 minus 2 end root minus square root of 9 over denominator negative 2 end fraction end cell row blank equals cell fraction numerator square root of 4 minus square root of 9 over denominator negative 2 end fraction end cell row blank equals cell fraction numerator 2 minus 3 over denominator negative 2 end fraction end cell row blank equals cell fraction numerator negative 1 over denominator negative 2 end fraction end cell row blank equals cell 1 half end cell end table end style 

Dengan demikian diperoleh begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator square root of 2 x minus 2 end root minus square root of 3 x end root over denominator 1 minus x end fraction equals 1 half end style

Oleh karena itu, jawaban yang benar adalah C.

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