Pertanyaan

Nilai x → 0 lim x 4 + 2 x − 4 − 2 x = ...

Nilai $x \to 0 lim \frac{4 + 2 x - 4 - 2 x}{x} = ...$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

nilai limit fungsi tersebut adalah 1.

Pembahasan

Dengan mensubstitusikan nilai x, diperoleh Karena hasil substitusi adalah bentuk tak tentu, maka limit tersebut dapat diselesaikan dengan metode kali akar sekawan: Jadi, nilai limit fungsi tersebut adalah 1.

Dengan mensubstitusikan nilai x, diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator square root of 4 plus 2 x end root minus square root of 4 minus 2 x end root over denominator x end fraction end cell equals cell fraction numerator square root of 4 plus 2 left parenthesis 0 right parenthesis end root minus square root of 4 minus 2 left parenthesis 0 right parenthesis end root over denominator 0 end fraction end cell row blank equals cell 0 over 0 end cell end table$

Karena hasil substitusi adalah bentuk tak tentu, maka limit tersebut dapat diselesaikan dengan metode kali akar sekawan:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator square root of 4 plus 2 x end root minus square root of 4 minus 2 x end root over denominator x end fraction cross times fraction numerator square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root over denominator square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses 4 plus 2 x close parentheses minus open parentheses 4 minus 2 x close parentheses over denominator x open parentheses square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 4 x over denominator x open parentheses square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 4 over denominator square root of 4 plus 2 x end root plus square root of 4 minus 2 x end root end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 4 plus 2 left parenthesis 0 right parenthesis end root plus square root of 4 minus 2 left parenthesis 0 right parenthesis end root end fraction end cell row blank equals cell 4 over 4 end cell row blank equals 1 end table$

Jadi, nilai limit fungsi tersebut adalah 1.