Roboguru

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Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 3 x over denominator x squared minus 9 end fraction end style .....

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack l i m with x rightwards arrow 3 below fraction numerator x squared minus 3 x over denominator x squared minus 9 end fraction end cell row blank equals cell stack l i m with x rightwards arrow 3 below fraction numerator x left parenthesis x minus 3 right parenthesis over denominator open parentheses x minus 3 close parentheses open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell stack l i m with x rightwards arrow 3 below fraction numerator x over denominator open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 3 over denominator 3 plus 3 end fraction end cell row blank equals cell 3 over 6 end cell end table 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Septianingsih

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 03 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Pembahasan Soal:

begin mathsize 14px style limit as straight x rightwards arrow 3 of open parentheses fraction numerator straight x squared plus 4 straight x minus 21 over denominator straight x minus 3 end fraction close parentheses equals limit as straight x rightwards arrow 3 of fraction numerator left parenthesis straight x plus 7 right parenthesis left parenthesis straight x minus 3 right parenthesis over denominator left parenthesis straight x minus 3 right parenthesis end fraction equals limit as straight x rightwards arrow 3 of open parentheses straight x plus 7 close parentheses equals 3 plus 7 equals 10 end style 

.  

0

Roboguru

Pembahasan Soal:

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

0

Roboguru

Nilai

Pembahasan Soal:

space limit as x rightwards arrow 3 of space fraction numerator 2 minus square root of x plus 1 end root over denominator x minus 3 end fraction space. space fraction numerator 2 plus square root of x plus 1 end root over denominator 2 plus square root of x plus 1 end root end fraction  space limit as x rightwards arrow 3 of space fraction numerator 4 minus left parenthesis x plus 1 right parenthesis over denominator open parentheses x minus 3 close parentheses open parentheses 2 plus square root of x plus 1 end root close parentheses end fraction  limit as x rightwards arrow 3 of fraction numerator up diagonal strike open parentheses negative x plus 3 close parentheses end strike over denominator negative up diagonal strike open parentheses negative x plus 3 close parentheses end strike open parentheses 2 plus square root of x plus 1 end root close parentheses end fraction  limit as x rightwards arrow 3 of fraction numerator 1 over denominator negative left parenthesis 2 plus square root of x plus 1 right parenthesis end root end fraction  equals fraction numerator 1 over denominator negative open parentheses 2 plus square root of 3 plus 1 end root close parentheses end fraction  equals fraction numerator 1 over denominator negative left parenthesis 2 plus 2 right parenthesis end fraction  equals negative 1 fourth

1

Roboguru

Pembahasan Soal:

begin mathsize 14px style x equals 3 end style disubtitusikan pada limit tersebut

begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator 3 x squared minus x minus 24 over denominator 2 x squared minus 3 x minus 9 end fraction equals fraction numerator 3 open parentheses 3 close parentheses squared minus 3 minus 24 over denominator 2 open parentheses 3 close parentheses squared minus 3 open parentheses 3 close parentheses minus 9 end fraction equals 0 over 0 end style  

Karena menghasilkan limit bentuk tak tentu maka akan ditentukan dengan metode pemfaktoran

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 3 x squared minus x minus 24 over denominator 2 x squared minus 3 x minus 9 end fraction end cell equals cell fraction numerator open parentheses 3 x plus 8 close parentheses up diagonal strike open parentheses x minus 3 close parentheses end strike over denominator open parentheses 2 x plus 3 close parentheses up diagonal strike open parentheses x minus 3 close parentheses end strike end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell fraction numerator 3 times 3 plus 8 over denominator 2 times 3 plus 3 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell 17 over 9 end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell 1 8 over 9 end cell end table end style    

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator 3 x squared minus x minus 24 over denominator 2 x squared minus 3 x minus 9 end fraction end style adalah begin mathsize 14px style 1 8 over 9 end style 

0

Roboguru

Pembahasan Soal:

Untuk mengetahui nilai dari limit fungsi aljabar yaitu dengan substitusi nilai x ke dalam fungsi tersebut sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator square root of x minus 4 end root end fraction end cell equals cell fraction numerator 4 squared minus 16 over denominator square root of 4 minus 4 end root end fraction end cell row blank equals cell fraction numerator 16 minus 16 over denominator square root of 0 end fraction end cell row blank equals cell fraction numerator 0 over denominator square root of 0 end fraction end cell row blank equals cell 0 over 0 end cell row blank equals cell tak space tentu end cell end table

Karena hasil dari substitusi yaitu tak tentu, maka harus menggunakan cara yang lain untuk menentukan nilai dari limit fungsi tersebut.

Ingat jika terdapat limit fungsi aljabar dengan bentuk rasional dengan penyebutnya bentuk akar maka dapat dilakukan perkalian sekawan terlebih dahulu sebelum melakukan substitusi dan ingat juga dengan menggunakan metode pemfaktoran sehinnga akan didapatkan hasil sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow 4 of fraction numerator straight x squared minus 16 over denominator square root of straight x minus 4 end root end fraction end cell equals cell limit as straight x rightwards arrow 4 of fraction numerator straight x squared minus 16 over denominator square root of straight x minus 4 end root end fraction cross times fraction numerator square root of straight x minus 4 end root over denominator square root of straight x minus 4 end root end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator open parentheses straight x squared minus 16 close parentheses open parentheses square root of straight x minus 4 end root close parentheses over denominator square root of straight x minus 4 end root cross times square root of straight x minus 4 end root end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator open parentheses straight x squared minus 16 close parentheses open parentheses square root of straight x minus 4 end root close parentheses over denominator straight x minus 4 end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x plus 4 right parenthesis left parenthesis x minus 4 right parenthesis left parenthesis square root of straight x minus 4 end root right parenthesis over denominator left parenthesis x minus 4 right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of fraction numerator left parenthesis straight x plus 4 right parenthesis up diagonal strike open parentheses straight x minus 4 close parentheses end strike left parenthesis square root of straight x minus 4 end root right parenthesis over denominator up diagonal strike straight x minus 4 end strike end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of left parenthesis straight x plus 4 right parenthesis left parenthesis square root of straight x minus 4 end root right parenthesis end cell row blank equals cell left parenthesis 4 plus 4 right parenthesis left parenthesis square root of 4 minus 4 end root right parenthesis end cell row blank equals cell 8 cross times square root of 0 end cell row blank equals cell 8 cross times 0 end cell row blank equals 0 end table

Jadi, dapat disimpulkan bahwa hasil dari  limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator square root of x minus 4 end root end fraction adalah 0.

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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