Roboguru

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator 4 x cubed minus 7 x squared plus 9 x over denominator x squared minus 3 x end fraction equals.... end style

Pembahasan Soal:

Limit fungsi aljabar dapat diselesaikan dengan cara pemfaktoran kemudian subsitusikan semua variabel dengan angka begin mathsize 14px style 0. end style 

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 4 x cubed minus 7 x squared plus 9 x over denominator x squared minus 3 x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator x open parentheses 4 x squared minus 7 x plus 9 close parentheses over denominator x open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 4 x squared minus 7 x plus 9 over denominator x minus 3 end fraction end cell row blank equals cell fraction numerator 9 over denominator negative 3 end fraction end cell row blank equals cell negative 3 end cell end table end style

Jadi,hasil dari limit tersebut yaitu begin mathsize 14px style negative 3. end style

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni UIN Walisongo Semarang

Terakhir diupdate 31 Maret 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Pembahasan Soal:

Menentukan limit dengan metode pemfaktoran

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator x squared plus 5 x plus 6 over denominator x plus 2 end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator open parentheses x plus 3 close parentheses open parentheses x plus 2 close parentheses over denominator x plus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 0 of open parentheses x plus 3 close parentheses end cell row blank equals cell 0 plus 3 end cell row blank equals 3 end table

Jadi, limit as x rightwards arrow 0 of fraction numerator x squared plus 5 x plus 6 over denominator x plus 2 end fraction equals 3.

Jadi, jawaban yang tepat adalah B.
 

0

Roboguru

Nilai yang tepat dari  adalah ...

Pembahasan Soal:

Nilai dari limit fungsi tersebut adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 5 of space fraction numerator x squared minus x minus 20 over denominator x minus 5 end fraction end cell equals cell limit as x rightwards arrow 5 of space fraction numerator open parentheses x minus 5 close parentheses open parentheses x plus 4 close parentheses over denominator x minus 5 end fraction end cell row blank equals cell limit as x rightwards arrow 5 of open parentheses space x plus 4 close parentheses end cell row blank equals cell 5 plus 4 end cell row blank equals 9 end table

Dengan demikian, nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 5 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared minus x minus 20 over denominator x minus 5 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 9 end table 

0

Roboguru

Tentukan nilai dari

Pembahasan Soal:

Perhatikan perhitungan berikut.

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 fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 over denominator x minus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 6 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction minus fraction numerator 2 over denominator left parenthesis x minus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 6 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction minus fraction numerator 2 left parenthesis x plus 1 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 6 minus 2 open parentheses x plus 1 close parentheses over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator 6 minus 2 x minus 2 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank blank cell stack equals lim with x rightwards arrow 2 below fraction numerator negative 2 x plus 4 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank blank cell stack equals lim with x rightwards arrow 2 below fraction numerator negative 2 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank blank cell stack equals lim with x rightwards arrow 2 below fraction numerator negative 2 over denominator left parenthesis x plus 1 right parenthesis end fraction times fraction numerator left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction end cell row blank blank cell stack equals lim with x rightwards arrow 2 below fraction numerator negative 2 over denominator left parenthesis x plus 1 right parenthesis end fraction times 1 end cell row blank equals cell fraction numerator negative 2 over denominator 2 plus 1 end fraction times 1 end cell row blank equals cell negative 2 over 3 end cell end table end style

Jadi, diperoleh begin mathsize 14px style limit as x rightwards arrow 2 of fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 over denominator x minus 2 end fraction equals negative 2 over 3 end style.

0

Roboguru

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack l i m with x rightwards arrow 4 below fraction numerator x squared minus 16 over denominator x squared minus x minus 12 end fraction end cell equals cell stack l i m with x rightwards arrow 4 below fraction numerator open parentheses x minus 4 close parentheses open parentheses x plus 4 close parentheses over denominator open parentheses x minus 4 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 4 below fraction numerator x plus 4 over denominator x plus 3 end fraction end cell row blank equals cell 8 over 7 end cell end table

Jadi, nilai limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator x squared minus x minus 12 end fraction8 over 7 adalah 8 over 7.

1

Roboguru

Nilai

Pembahasan Soal:

Dengan menggunakan metode pemfaktoran diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 27 of fraction numerator x minus 27 over denominator x to the power of begin display style 1 third end style end exponent minus 3 end fraction end cell equals cell limit as x rightwards arrow 27 of fraction numerator open parentheses x to the power of begin display style 1 third end style end exponent minus 3 close parentheses open parentheses x to the power of begin display style 2 over 3 end style end exponent plus 3 x to the power of begin display style 1 third end style end exponent plus 9 close parentheses over denominator x to the power of begin display style 1 third end style end exponent minus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 27 of space x to the power of 2 over 3 end exponent plus 3 x to the power of 1 third end exponent plus 9 end cell row blank equals cell space 27 to the power of 2 over 3 end exponent plus 3 open parentheses 27 to the power of 1 third end exponent close parentheses plus 9 end cell row blank equals cell 9 plus 3 open parentheses 3 close parentheses plus 9 end cell row blank equals cell 9 plus 9 plus 9 end cell row blank equals 27 end table

Dengan demikian nilai dari limit as x rightwards arrow 27 of fraction numerator x minus 27 over denominator x to the power of begin display style 1 third end style end exponent minus 3 end fraction equals 27.

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Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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