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Hitunglah: a. x→3lim​x3−7x2+15x−9x3−8x2+21x−18​

Pertanyaan

Hitunglah:

a. limit as x rightwards arrow 3 of fraction numerator x cubed minus 8 x squared plus 21 x minus 18 over denominator x cubed minus 7 x squared plus 15 x minus 9 end fraction  

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai dari limit as x rightwards arrow 3 of fraction numerator x cubed minus 8 x squared plus 21 x minus 18 over denominator x cubed minus 7 x squared plus 15 x minus 9 end fraction adalah 1 half 

Pembahasan

Selesaikan limit tersebut menggunakan metode substitusi terlebih dahulu

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x cubed minus 8 x squared plus 21 x minus 18 over denominator x cubed minus 7 x squared plus 15 x minus 9 end fraction end cell equals cell fraction numerator 3 cubed minus 8 left parenthesis 3 right parenthesis squared plus 21 left parenthesis 3 right parenthesis minus 18 over denominator 3 cubed minus 7 left parenthesis 3 right parenthesis squared plus 15 left parenthesis 3 right parenthesis minus 9 end fraction end cell row blank equals cell fraction numerator 27 minus 72 plus 63 minus 18 over denominator 27 minus 63 plus 45 minus 9 end fraction end cell row blank equals cell 0 over 0 end cell end table 

Karena jika diselesaikan dengan substitusi langsung hasilnya bentuk tak tentu maka kita harus menyelesaikannya dengan metode yang lain.

Ingat kembali bahwa

limit as x rightwards arrow c of space fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals limit as x rightwards arrow c of space fraction numerator f apostrophe apostrophe left parenthesis x right parenthesis over denominator g apostrophe apostrophe left parenthesis x right parenthesis end fraction  

Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x cubed minus 8 x squared plus 21 x minus 18 over denominator x cubed minus 7 x squared plus 15 x minus 9 end fraction end cell equals cell limit as x rightwards arrow 3 of space fraction numerator 3 x squared minus 16 x plus 21 over denominator 3 x squared minus 14 x plus 15 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of space fraction numerator 6 x minus 16 over denominator 6 x minus 14 end fraction end cell row blank equals cell fraction numerator 6 left parenthesis 3 right parenthesis minus 16 over denominator 6 left parenthesis 3 right parenthesis minus 14 end fraction end cell row blank equals cell fraction numerator 18 minus 16 over denominator 18 minus 14 end fraction end cell row blank equals cell 2 over 4 end cell row blank equals cell 1 half end cell end table 

Jadi, nilai dari limit as x rightwards arrow 3 of fraction numerator x cubed minus 8 x squared plus 21 x minus 18 over denominator x cubed minus 7 x squared plus 15 x minus 9 end fraction adalah 1 half 

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