Pertanyaan

x → 1 lim 1 − x x + 2 − 4 x − 1 = ...

$x \to 1 lim \frac{x + 2 - 4 x - 1}{1 - x} = ...$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

x → 1 lim 1 − x x + 2 − 4 x − 1 = 2 1 3 .

x \to 1 lim \frac{x + 2 - 4 x - 1}{1 - x} = \frac{1}{2} 3

Pembahasan

Dengan demikian x → 1 lim 1 − x x + 2 − 4 x − 1 = 2 1 3 .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of fraction numerator square root of x plus 2 end root minus square root of 4 x minus 1 end root over denominator 1 minus x end fraction cross times fraction numerator square root of x plus 2 end root plus square root of 4 x minus 1 end root over denominator square root of x plus 2 end root plus square root of 4 x minus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis x plus 2 right parenthesis minus left parenthesis 4 x minus 1 right parenthesis over denominator left parenthesis 1 minus x right parenthesis left parenthesis square root of x plus 2 end root plus square root of 4 x minus 1 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator negative 3 x plus 3 over denominator left parenthesis 1 minus x right parenthesis left parenthesis square root of x plus 2 end root plus square root of 4 x minus 1 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 3 up diagonal strike left parenthesis 1 minus x right parenthesis end strike over denominator up diagonal strike left parenthesis 1 minus x right parenthesis end strike left parenthesis square root of x plus 2 end root plus square root of 4 x minus 1 end root right parenthesis end fraction end cell row blank equals cell fraction numerator 3 over denominator left parenthesis square root of 1 plus 2 end root plus square root of 4 left parenthesis 1 right parenthesis minus 1 end root end fraction end cell row blank equals cell fraction numerator 3 over denominator square root of 3 plus square root of 3 end fraction end cell row blank equals cell fraction numerator 3 over denominator 2 square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell 3 over 6 square root of 3 end cell row blank equals cell 1 half square root of 3 end cell end table end style$

Dengan demikian $x \to 1 lim \frac{x + 2 - 4 x - 1}{1 - x} = \frac{1}{2} 3$ .