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Hitunglah nilai limit fungsi berikut:   x→1lim​x−164​(x+31​−3x+52​)

Pertanyaan

Hitunglah nilai limit fungsi berikut:
 

begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 64 over denominator x minus 1 end fraction open parentheses fraction numerator 1 over denominator x plus 3 end fraction minus fraction numerator 2 over denominator 3 x plus 5 end fraction close parentheses end style

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Kita selesaikan limit tersebut dengan metode substitusi terlebih dahulu.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator 64 over denominator x minus 1 end fraction open parentheses fraction numerator 1 over denominator x plus 3 end fraction minus fraction numerator 2 over denominator 3 x plus 5 end fraction close parentheses end cell equals cell fraction numerator 64 over denominator 1 minus 1 end fraction open parentheses fraction numerator 1 over denominator 1 plus 3 end fraction minus fraction numerator 2 over denominator 3 left parenthesis 1 right parenthesis plus 5 end fraction close parentheses end cell row blank equals cell 0 over 0 end cell end table  

Karena jika disubstitusikan menghasilkan bentuk tak tentu maka selesaikan limit tersebut dengan metode pemfaktoran seperti berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator 64 over denominator x minus 1 end fraction open parentheses fraction numerator 1 over denominator x plus 3 end fraction minus fraction numerator 2 over denominator 3 x plus 5 end fraction close parentheses end cell equals cell limit as x rightwards arrow 1 of fraction numerator 64 over denominator x minus 1 end fraction open parentheses fraction numerator 3 x plus 5 minus 2 left parenthesis x plus 3 right parenthesis over denominator left parenthesis x plus 3 right parenthesis left parenthesis 3 x plus 5 right parenthesis end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 64 over denominator x minus 1 end fraction open parentheses fraction numerator x minus 1 over denominator left parenthesis x plus 3 right parenthesis left parenthesis 3 x plus 5 right parenthesis end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 64 over denominator left parenthesis x plus 3 right parenthesis left parenthesis 3 x plus 5 right parenthesis end fraction end cell row blank equals cell fraction numerator 64 over denominator left parenthesis 1 plus 3 right parenthesis left parenthesis 3 left parenthesis 1 right parenthesis plus 5 right parenthesis end fraction end cell row blank equals cell fraction numerator 64 over denominator 4 times 8 end fraction end cell row blank equals 2 end table end style 

Jadi, nilai limit fungsi tersebut adalah 2.

 

 

17

5.0 (2 rating)

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