Roboguru

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

Pembahasan Soal:

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

 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Eka

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 05 Oktober 2021

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Pertanyaan yang serupa

Nilai dari x→4lim​x2−16x2−4x​=...

Pembahasan Soal:

Jika menentukan nilai limit fungsi tersebut dengan menggunakan metode subsitusi maka akan diperoleh begin mathsize 14px style 0 over 0 end style seperti berikut ini:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of fraction numerator x squared minus 4 x over denominator x squared minus 16 end fraction end cell equals cell fraction numerator 4 squared minus 4 open parentheses 4 close parentheses over denominator 4 squared minus 16 end fraction end cell row blank equals cell fraction numerator 16 minus 16 over denominator 16 minus 16 end fraction end cell row blank equals cell 0 over 0 end cell end table end style 

Oleh sebab itu, untuk menentukan nilai limit tersebut dapat menggunakan metode pemfaktoran sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of space fraction numerator x squared minus 4 x over denominator x squared minus 16 end fraction end cell equals cell limit as x rightwards arrow 4 of fraction numerator x open parentheses x minus 4 close parentheses over denominator open parentheses x plus 4 close parentheses open parentheses x minus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator x over denominator x plus 4 end fraction end cell row blank equals cell fraction numerator 4 over denominator 4 plus 4 end fraction end cell row blank equals cell 4 over 8 end cell row blank equals cell 1 half end cell row blank blank blank end table end style 

Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Hitunglah nilai limit berikut ini. x→−3lim​x+3x2−9​

Pembahasan Soal:

Nilai dari begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator x squared minus 9 over denominator x plus 3 end fraction end style dapat ditentukan menggunakan cara pemfaktoran sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 3 of fraction numerator x squared minus 9 over denominator x plus 3 end fraction end cell equals cell limit as x rightwards arrow negative 3 of fraction numerator open parentheses x plus 3 close parentheses open parentheses x minus 3 close parentheses over denominator x plus 3 end fraction end cell row blank equals cell limit as x rightwards arrow negative 3 of open parentheses x minus 3 close parentheses end cell row blank equals cell negative 3 minus 3 end cell row blank equals cell negative 6 end cell end table end style

Dengan demikian, nilai begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator x squared minus 9 over denominator x plus 3 end fraction equals negative 6 end style

0

Roboguru

x→3lim​x+1​−7−x​x2−9​=...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 3 of fraction numerator straight x squared minus 9 over denominator square root of straight x plus 1 end root minus square root of 7 minus straight x end root end fraction end cell equals cell limit as straight x rightwards arrow 3 of fraction numerator begin display style straight x squared minus 9 end style over denominator begin display style square root of straight x plus 1 end root minus square root of 7 minus straight x end root end style end fraction. fraction numerator begin display style square root of straight x plus 1 end root plus square root of 7 minus straight x end root end style over denominator begin display style square root of straight x plus 1 end root plus square root of 7 minus straight x end root end style end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator begin display style open parentheses straight x squared minus 9 close parentheses open parentheses square root of straight x plus 1 end root plus square root of 7 minus straight x end root close parentheses end style over denominator begin display style open parentheses square root of straight x plus 1 end root close parentheses squared minus open parentheses square root of 7 minus straight x end root close parentheses squared end style end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator begin display style open parentheses straight x squared minus 9 close parentheses open parentheses square root of straight x plus 1 end root plus square root of 7 minus straight x end root close parentheses end style over denominator begin display style open parentheses straight x plus 1 close parentheses minus open parentheses 7 minus straight x close parentheses end style end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator begin display style open parentheses straight x squared minus 9 close parentheses open parentheses square root of straight x plus 1 end root plus square root of 7 minus straight x end root close parentheses end style over denominator begin display style 2 straight x minus 6 end style end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator begin display style open parentheses straight x minus 3 close parentheses open parentheses straight x plus 3 close parentheses open parentheses square root of straight x plus 1 end root plus square root of 7 minus straight x end root close parentheses end style over denominator begin display style 2 open parentheses straight x minus 3 close parentheses end style end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator begin display style open parentheses straight x plus 3 close parentheses open parentheses square root of straight x plus 1 end root plus square root of 7 minus straight x end root close parentheses end style over denominator begin display style 2 end style end fraction end cell row blank equals cell fraction numerator begin display style open parentheses 3 plus 3 close parentheses open parentheses square root of 3 plus 1 end root plus square root of 7 minus 3 end root close parentheses end style over denominator begin display style 2 end style end fraction end cell row blank equals cell fraction numerator begin display style 6 open parentheses square root of 4 plus square root of 4 close parentheses end style over denominator begin display style 2 end style end fraction end cell row blank equals cell box enclose 12 end cell end table

0

Roboguru

Nilai dari x→−2lim​2x+48x2+14x−4​=….

Pembahasan Soal:

0

Roboguru

Hitunglah nilai limit berikut ini. x→2lim​x−22x2−5x+2​

Pembahasan Soal:

Nilai dari begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator 2 x squared minus 5 x plus 2 over denominator x minus 2 end fraction end style dapat ditentukan dengan menggunakan metode pemfaktoran.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator 2 x squared minus 5 x plus 2 over denominator x minus 2 end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator open parentheses 2 x minus 1 close parentheses open parentheses x minus 2 close parentheses over denominator x minus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses 2 x minus 1 close parentheses end cell row blank equals cell 2 open parentheses 2 close parentheses minus 1 end cell row blank equals 3 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 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x squared minus 5 x plus 2 over denominator x minus 2 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 3 end table end style

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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