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Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator 2 x squared minus 3 x minus 35 over denominator x squared minus 5 x end fraction equals space... end style 

Pembahasan Soal:

Limit fungsi aljabar adalah menentukan nilai fungsi aljabar jika peubah fungsi tersebut mendekati nilai tertentu.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 5 of space fraction numerator 2 x squared minus 3 x minus 35 over denominator x squared minus 5 x end fraction end cell equals cell limit as x rightwards arrow 5 of space fraction numerator left parenthesis 2 x plus 7 right parenthesis left parenthesis x minus 5 right parenthesis over denominator x open parentheses x minus 5 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 5 of space fraction numerator left parenthesis 2 x plus 7 right parenthesis up diagonal strike left parenthesis x minus 5 right parenthesis end strike over denominator x up diagonal strike open parentheses x minus 5 close parentheses end strike end fraction end cell row blank equals cell limit as x rightwards arrow 5 of space fraction numerator 2 x plus 7 over denominator x end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 5 right parenthesis plus 7 over denominator 5 end fraction end cell row blank equals cell fraction numerator 10 plus 7 over denominator 5 end fraction end cell row blank equals cell 17 over 5 end cell end table end style

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 5 of space fraction numerator 2 x squared minus 3 x minus 35 over denominator x squared minus 5 x end fraction end style adalah begin mathsize 14px style 17 over 5 end style

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Dwi

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 30 Maret 2021

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Pertanyaan yang serupa

...

Pembahasan Soal:

Pertama substitusi nilai x,

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator 2 x squared minus 2 x over denominator 2 x end fraction equals 0 over 0 end style

Karena hasil substitusinya adalah bentuk tak tentu, maka nilai limit dapat ditentukan dengan pemfaktoran sebagai berikut

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

Jadi, hasil limitnya adalah begin mathsize 14px style negative 1 end style.

 

Roboguru

Tentukan nilai limit berikut. a.

Pembahasan Soal:

Nilai limit tidak boleh berupa begin mathsize 14px style 0 over 0 end style.

Langkah pertama menentukan limit aljabar adalah dengan menyubstitusikan nilai begin mathsize 14px style x end style pada fungsi.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of left parenthesis x squared minus 5 x plus 8 right parenthesis end cell equals cell 1 squared minus 5 times 1 plus 8 end cell row blank equals cell 1 minus 5 plus 8 end cell row blank equals 4 end table end style 

Jika hasilnya bukan begin mathsize 14px style 0 over 0 end style, maka nilai limit telah ditemukan.

Jadi, begin mathsize 14px style limit as x rightwards arrow 1 of left parenthesis x squared minus 5 x plus 8 right parenthesis equals 4 end style.

Roboguru

Pembahasan Soal:

begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction equals limit as x rightwards arrow negative 3 of fraction numerator 2 x open parentheses x plus 3 close parentheses over denominator 5 open parentheses x plus 3 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow negative 3 of fraction numerator 2 x over denominator 5 end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 open parentheses negative 3 close parentheses over denominator 5 end fraction space space space space space space space space space space space space space space space space space space space space space space space space equals negative 6 over 5 end style

Roboguru

...

Pembahasan Soal:

Nilai dari limit as x rightwards arrow 1 of space fraction numerator open parentheses 3 x minus 1 close parentheses squared minus 4 over denominator x squared plus 4 x minus 5 end fraction:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of space fraction numerator open parentheses 3 x minus 1 close parentheses squared minus 4 over denominator x squared plus 4 x minus 5 end fraction end cell equals cell limit as x rightwards arrow 1 of space fraction numerator 9 x squared minus 6 x plus 1 minus 4 over denominator x squared plus 4 x minus 5 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of space fraction numerator 9 x squared minus 6 x minus 3 over denominator x squared plus 4 x minus 5 end fraction end cell row blank equals cell limit as x rightwards arrow 1 of space fraction numerator open parentheses 9 x plus 3 close parentheses open parentheses x minus 1 close parentheses over denominator open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 1 of space fraction numerator open parentheses 9 x plus 3 close parentheses up diagonal strike open parentheses x minus 1 close parentheses end strike over denominator open parentheses x plus 5 close parentheses up diagonal strike open parentheses x minus 1 close parentheses end strike end fraction end cell row blank equals cell limit as x rightwards arrow 1 of space fraction numerator open parentheses 9 x plus 3 close parentheses over denominator open parentheses x plus 5 close parentheses end fraction end cell row blank equals cell fraction numerator 9 open parentheses 1 close parentheses plus 3 over denominator 1 plus 5 end fraction end cell row blank equals cell fraction numerator 9 plus 3 over denominator 6 end fraction end cell row blank equals cell 12 over 6 end cell row blank equals 2 end table 

Jadi, nilai dari limit as x rightwards arrow 1 of space fraction numerator open parentheses 3 x minus 1 close parentheses squared minus 4 over denominator x squared plus 4 x minus 5 end fraction adalah 2.

Roboguru

Pembahasan Soal:

Nilai dari begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator x minus 1 over denominator x squared minus 1 end fraction end style:

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

Jadi, nilai dari begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator x minus 1 over denominator x squared minus 1 end fraction end style adalah begin mathsize 14px style 1 half end style

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