Jikax→4lim​x−4ax+b−x​​=43​, nilai a+b adalah ...

Pertanyaan

Jikalimit as x rightwards arrow 4 of fraction numerator a x plus b minus square root of x over denominator x minus 4 end fraction equals 3 over 4, nilai begin mathsize 14px style a plus b end style adalah ...

  1. begin mathsize 14px style negative 2 end style 

  2. begin mathsize 14px style negative 1 end style 

  3. begin mathsize 14px style 1 end style  

  4. begin mathsize 14px style 2 end style 

  5. begin mathsize 14px style 3 end style 

H. Firmansyah

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B

Pembahasan

Perhatikan perhitungan berikut limit as x rightwards arrow 4 of fraction numerator a x plus b minus square root of x over denominator x minus 4 end fraction equals 3 over 4.

Langkah ke 1, dengan aturan L'Hopital diperoleh

space space space space space space limit as straight x rightwards arrow 4 of fraction numerator open parentheses straight a minus begin display style fraction numerator 1 over denominator 2 square root of straight x end fraction end style close parentheses over denominator 1 end fraction equals 3 over 4 left right double arrow straight a minus fraction numerator 1 over denominator 2 square root of 4 end fraction equals 3 over 4 left right double arrow straight a minus 1 fourth equals 3 over 4 left right double arrow straight a equals 1

Kemudian, diperoleh perhitungan

limit as straight x rightwards arrow 4 of fraction numerator ax plus straight b minus square root of straight x over denominator straight x minus 4 end fraction equals 3 over 4 limit as straight x rightwards arrow 4 of fraction numerator straight x plus straight b minus square root of straight x over denominator straight x minus 4 end fraction equals 3 over 4 fraction numerator 4 plus straight b minus square root of 4 over denominator straight x minus 4 end fraction equals 3 over 4 fraction numerator 2 plus straight b space over denominator straight x minus 4 end fraction space 2 plus straight b space harus space kelipatan space open parentheses straight x minus 4 close parentheses 2 plus straight b equals 0 straight b equals negative 2

Dengan demikian, diperoleh  straight a plus straight b equals 1 minus 2 equals negative 1.

Jadi, jawaban yang tepat adalah B

355

4.6 (34 rating)

Alya Widya Ananta

Bantu banget Makasih ❤️

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