Pertanyaan

Nilai dari x → 4 lim 3 x + 4 − 5 x − 4 2 x + 1 − x + 5 = …

Nilai dari $x \to 4 lim \frac{2 x + 1 - x + 5}{3 x + 4 - 5 x - 4} = \dots$

A. Acfreelance

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

nilai dari limit tersebut adalah

nilai dari limit tersebut adalah negative 5 over 3

Pembahasan

Pada soal ini, metode yang sesuai adalah dengan pengalian faktor sekawan karena apabila dikerjakan dengan metode substitusi akan menghasilkan bilangan tak hingga. Jadi, nilai dari limit tersebut adalah

Pada soal ini, metode yang sesuai adalah dengan pengalian faktor sekawan karena apabila dikerjakan dengan metode substitusi akan menghasilkan bilangan tak hingga.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of fraction numerator square root of 2 x plus 1 end root minus square root of x plus 5 end root over denominator square root of 3 x plus 4 end root minus square root of 5 x minus 4 end root end fraction end cell equals cell limit as x rightwards arrow 4 of fraction numerator square root of 2 x plus 1 end root minus square root of x plus 5 end root over denominator square root of 3 x plus 4 end root minus square root of 5 x minus 4 end root end fraction times fraction numerator square root of 2 x plus 1 end root plus square root of x plus 5 end root over denominator square root of 2 x plus 1 end root plus square root of x plus 5 end root end fraction times fraction numerator square root of 3 x plus 4 end root plus square root of 5 x minus 4 end root over denominator square root of 3 x plus 4 end root plus square root of 5 x minus 4 end root end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator open parentheses 2 x plus 1 minus x plus 5 close parentheses times square root of 3 x plus 4 end root plus square root of 5 x minus 4 end root over denominator open parentheses 3 x plus 4 minus 5 x minus 4 close parentheses times square root of 2 x plus 1 end root plus square root of x plus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator open parentheses x plus 6 close parentheses times square root of 3 x plus 4 end root plus square root of 5 x minus 4 end root over denominator open parentheses negative 2 x close parentheses times square root of 2 x plus 1 end root plus square root of x plus 5 end root end fraction end cell row blank equals cell fraction numerator open parentheses 4 plus 6 close parentheses times square root of 3 open parentheses 4 close parentheses plus 4 end root plus square root of 5 open parentheses 4 close parentheses minus 4 end root over denominator open parentheses negative 2 open parentheses 4 close parentheses close parentheses times square root of 2 open parentheses 4 close parentheses plus 1 end root plus square root of open parentheses 4 close parentheses plus 5 end root end fraction end cell row blank equals cell fraction numerator 10 open parentheses square root of 12 plus 4 end root plus square root of 20 minus 4 end root close parentheses over denominator negative 8 open parentheses square root of 8 plus 1 end root plus square root of 4 plus 5 end root close parentheses end fraction end cell row blank equals cell fraction numerator 10 open parentheses square root of 16 plus square root of 16 close parentheses over denominator negative 8 open parentheses square root of 9 plus square root of 9 close parentheses end fraction end cell row blank equals cell fraction numerator 10 open parentheses 4 plus 4 close parentheses over denominator negative 8 open parentheses 3 plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 10 open parentheses 8 close parentheses over denominator negative 8 open parentheses 6 close parentheses end fraction end cell row blank equals cell negative 80 over 48 end cell row blank equals cell negative 5 over 3 end cell end table$

Jadi, nilai dari limit tersebut adalah negative 5 over 3