Pertanyaan

Nilai dari x → 2 lim x − 2 3 x − 4 − x

Nilai dari $x \to 2 lim \frac{3 x - 4 - x}{x - 2}$

N. Sari

Master Teacher

Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Pembahasan

Nilai limit tersebut dapat diketahui dengan mengalikan akar sekawan pembilangnya. Sehingga : Maka, nilai dari .

Nilai limit tersebut dapat diketahui dengan mengalikan akar sekawan pembilangnya. Sehingga :

$limit as x rightwards arrow 2 of fraction numerator square root of 3 x minus 4 end root minus square root of x over denominator x minus 2 end fraction cross times fraction numerator square root of 3 x minus 4 end root plus square root of x over denominator square root of 3 x minus 4 end root plus square root of x end fraction equals limit as x rightwards arrow 2 of fraction numerator 3 x minus 4 minus x over denominator open parentheses x minus 2 close parentheses open parentheses square root of 3 x minus 4 end root plus square root of x close parentheses end fraction equals limit as x rightwards arrow 2 of fraction numerator 2 x minus 4 over denominator open parentheses x minus 2 close parentheses open parentheses square root of 3 x minus 4 end root plus square root of x close parentheses end fraction equals limit as x rightwards arrow 2 of fraction numerator 2 up diagonal strike open parentheses x minus 2 close parentheses end strike over denominator up diagonal strike open parentheses x minus 2 close parentheses end strike open parentheses square root of 3 x minus 4 end root plus square root of x close parentheses end fraction equals limit as x rightwards arrow 2 of fraction numerator 2 over denominator square root of 3 x minus 4 end root plus square root of x end fraction equals fraction numerator 2 over denominator square root of 3 left parenthesis 2 right parenthesis minus 4 end root plus square root of 2 end fraction equals fraction numerator 2 over denominator square root of 2 plus square root of 2 end fraction equals fraction numerator 2 over denominator 2 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals fraction numerator 2 square root of 2 over denominator 4 end fraction equals 1 half square root of 2$

Maka, nilai dari $limit as x rightwards arrow 2 of fraction numerator square root of 3 x minus 4 end root minus square root of x over denominator x minus 2 end fraction equals 1 half square root of 2$ .