Pertanyaan

Tentukan nilai limit fungsi berikut. x → 1 lim x 2 + 3 − 2 x − 1

Tentukan nilai limit fungsi berikut.

$x \to 1 lim \frac{x - 1}{x ^{2} + 3 - 2}$

L. Sibuea

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

nilai dari adalah

nilai dari $limit as x rightwards arrow 1 of space fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction$ adalah

Pembahasan

Dengan menggunakan metode mengalikan akar sekawan, maka nilai adalah Dengan demikian, nilai dari adalah

Dengan menggunakan metode mengalikan akar sekawan, maka nilai $limit as x rightwards arrow 1 of space fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction$ adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of space fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction end cell equals cell limit as x rightwards arrow 1 of space fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction space times space fraction numerator square root of x squared plus 3 end root plus 2 over denominator square root of x squared plus 3 end root plus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of space fraction numerator open parentheses x minus 1 space close parentheses times square root of x squared plus 3 end root plus 2 over denominator open parentheses x squared plus 3 close parentheses minus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of space fraction numerator open parentheses x minus 1 space close parentheses times square root of x squared plus 3 end root plus 2 over denominator x squared minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of space fraction numerator open parentheses x minus 1 space close parentheses times square root of x squared plus 3 end root plus 2 over denominator open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of space fraction numerator square root of x squared plus 3 end root plus 2 over denominator open parentheses x plus 1 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 1 squared plus 3 end root plus 2 over denominator 1 plus 1 end fraction equals fraction numerator square root of 4 plus 2 over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 plus 2 over denominator 2 end fraction equals 4 over 2 end cell row cell limit as x rightwards arrow 1 of space fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction end cell equals 2 end table$

Dengan demikian, nilai dari $limit as x rightwards arrow 1 of space fraction numerator x minus 1 over denominator square root of x squared plus 3 end root minus 2 end fraction$ adalah