Pertanyaan

Jika x → 4 lim x − 4 a x + b − x = 2 1 maka a + b = …

Jika $x \to 4 lim \frac{a x + b - x}{x - 4} = \frac{1}{2}$ maka $a + b = \dots$

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai

Pembahasan

Penyelesaian dari limit tersebut dapat menggunakan metode L'Hospital sebagai berikut. Dari uraian di atas diperoleh nilai-nilai berikut. Nilai Dengan demikian, nilai

Penyelesaian dari limit tersebut dapat menggunakan metode L'Hospital sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator square root of a x plus b end root minus square root of x over denominator x minus 4 end fraction end cell equals cell 1 half end cell row cell limit as x rightwards arrow 4 of space fraction numerator begin display style fraction numerator a over denominator 2 square root of a x plus b end root end fraction end style minus begin display style fraction numerator 1 over denominator 2 square root of x end fraction end style over denominator 1 end fraction end cell equals cell 1 half end cell row cell limit as x rightwards arrow 4 of space fraction numerator a over denominator 2 square root of a x plus b end root end fraction minus fraction numerator 1 over denominator 2 square root of x end fraction end cell equals cell 1 half end cell row cell fraction numerator a over denominator 2 square root of 4 a plus b end root end fraction minus fraction numerator 1 over denominator 2 square root of 4 end fraction end cell equals cell 1 half end cell row cell fraction numerator a over denominator 2 square root of 4 a plus b end root end fraction minus 1 fourth end cell equals cell 1 half end cell row cell fraction numerator a over denominator 2 square root of 4 a plus b end root end fraction end cell equals cell 1 half plus 1 fourth end cell row cell fraction numerator a over denominator 2 square root of 4 a plus b end root end fraction end cell equals cell 3 over 4 end cell row cell fraction numerator a over denominator square root of 4 a plus b end root end fraction end cell equals cell 3 over 2 end cell end table$

Dari uraian di atas diperoleh nilai-nilai berikut.

a equals 3

Nilai a plus b equals 3 plus open parentheses negative 8 close parentheses equals negative 5

Dengan demikian, nilai a plus b equals negative 5