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Hitunglah nilai limit berikut ini. x→3lim​x−3x3−x2−6x​

Pertanyaan

Hitunglah nilai limit berikut ini.

begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x cubed minus x squared minus 6 x over denominator x minus 3 end fraction end style

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Nilai dari begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x cubed minus x squared minus 6 x over denominator x minus 3 end fraction end style dapat ditentukan dengan menggunakan metode pemfaktoran sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x cubed minus x squared minus 6 x over denominator x minus 3 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator x open parentheses x squared minus x minus 6 close parentheses over denominator x minus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator x open parentheses x plus 2 close parentheses open parentheses x minus 3 close parentheses over denominator x minus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of x open parentheses x plus 2 close parentheses end cell row blank equals cell 3 open parentheses 3 plus 2 close parentheses end cell row blank equals 15 end table end style

Dengan demikian, nilai begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x cubed minus x squared minus 6 x over denominator x minus 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 15 end table end style

 

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