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x→∞lim​(2x​+1)−4x−3x​+2​=...

Pertanyaan

limit as x rightwards arrow infinity of open parentheses 2 square root of x plus 1 close parentheses minus square root of 4 x minus 3 square root of x plus 2 end root equals...     

  1. negative infinity  

  2. negative 3 over 4 

  3. 1 

  4. 7 over 4 

  5. infinity 

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat! 

limit as x rightwards arrow infinity of square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator b minus q over denominator 2 square root of 2 end fraction comma space jika space a equals p end cell row cell infinity space jika comma space a greater than p end cell row cell negative infinity space jika comma space a less than p end cell end table close 

Perhatikan perhitungan berikut! 

limit as x rightwards arrow infinity of open parentheses 2 square root of x plus 1 close parentheses minus square root of 4 x minus 3 square root of x plus 2 end root equals limit as x rightwards arrow infinity of square root of open parentheses 2 square root of x plus 1 close parentheses squared end root minus square root of 4 x minus 3 square root of x plus 2 end root equals limit as x rightwards arrow infinity of square root of 4 x plus 4 square root of x plus 1 end root minus square root of 4 x minus 3 square root of x plus 2 end root equals fraction numerator b minus q over denominator 2 square root of a end fraction equals fraction numerator 4 minus open parentheses negative 3 close parentheses over denominator 2 square root of 4 end fraction equals fraction numerator 4 plus 3 over denominator 2 times 2 end fraction equals 7 over 4        

Oleh karena itu, jawaban yang benar adalah D.

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