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Nilai dari x→2lim​x2+2x−8x2+x−6​ adalah ...

Pertanyaan

Nilai dari limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x minus 8 end fraction adalah ...

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

 limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x minus 8 end fraction equals 5 over 6

Pembahasan

Substitusi x equals 2, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x minus 8 end fraction end cell equals cell fraction numerator open parentheses 2 close parentheses squared plus open parentheses 2 close parentheses minus 6 over denominator open parentheses 2 close parentheses squared plus 2 open parentheses 2 close parentheses minus 8 end fraction end cell row blank equals cell fraction numerator 4 plus 2 minus 6 over denominator 4 plus 4 minus 8 end fraction end cell row blank equals cell 0 over 0 end cell end table 

Hasilnya bentuk tak tentu, maka limit tersebut dapat diselesaikan dengan metode pemfaktoran seperti di bawah ini 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x minus 8 end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x plus 3 close parentheses open parentheses x minus 2 close parentheses over denominator open parentheses x plus 4 close parentheses open parentheses x minus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses x plus 3 close parentheses over denominator open parentheses x plus 4 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 2 close parentheses plus 3 over denominator open parentheses 2 close parentheses plus 4 end fraction end cell row blank equals cell 5 over 6 end cell end table 

Jadi, limit as x rightwards arrow 2 of fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x minus 8 end fraction equals 5 over 6

122

3.3 (3 rating)

Muhammad Fauzan Wijaya

Jawaban tidak sesuai

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