Tentukanlah x→4lim​ x2−3x−43x2−14x+8​=...

Pertanyaan

Tentukanlah limit as x rightwards arrow 4 of space fraction numerator 3 x squared minus 14 x plus 8 over denominator x squared minus 3 x minus 4 end fraction equals...

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

nilai dari limit as x rightwards arrow 4 of space fraction numerator 3 x squared minus 14 x plus 8 over denominator x squared minus 3 x minus 4 end fraction adalah 2.

Pembahasan

Perhatikan perhitungan berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator 3 x squared minus 14 x plus 8 over denominator x squared minus 3 x minus 4 end fraction end cell equals cell fraction numerator 3 open parentheses 4 close parentheses squared minus 14 open parentheses 4 close parentheses plus 8 over denominator open parentheses 4 close parentheses squared minus 3 open parentheses 4 close parentheses minus 4 end fraction end cell row blank equals cell fraction numerator 48 minus 56 plus 8 over denominator 16 minus 12 minus 4 end fraction end cell row blank equals cell 0 over 0 end cell end table

Karena jika disubtitusikan nilai x equals 4 menghsilkan bentuk tak tentu 0 over 0. Maka kita gunakan metode pemfaktoran

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator 3 x squared minus 14 x plus 8 over denominator x squared minus 3 x minus 4 end fraction end cell equals cell limit as x rightwards arrow 4 of space fraction numerator open parentheses 3 x minus 2 close parentheses up diagonal strike open parentheses x minus 4 close parentheses end strike over denominator open parentheses x plus 1 close parentheses up diagonal strike open parentheses x minus 4 close parentheses end strike end fraction end cell row blank equals cell fraction numerator 3 open parentheses 4 close parentheses minus 2 over denominator 4 plus 1 end fraction end cell row blank equals cell 10 over 5 end cell row blank equals 2 end table

Dengan demikian nilai dari limit as x rightwards arrow 4 of space fraction numerator 3 x squared minus 14 x plus 8 over denominator x squared minus 3 x minus 4 end fraction adalah 2.

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Pertanyaan serupa

Hitunglah nilai limit berikut! 4.    x→1lim​x−1x2+4x−5​=....

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