Pertanyaan

Nilai x → 12 lim 2 x + 1 − 5 x − 12 adalah ....

Nilai $x \to 12 lim \frac{x - 12}{2 x + 1 - 5}$ adalah ....

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $begin mathsize 14px style stack bold l bold i bold m with bold x bold rightwards arrow bold 12 below bold space fraction numerator square root of bold x bold minus square root of bold 12 over denominator square root of bold 2 bold x bold plus bold 1 end root bold minus bold 5 end fraction end style$ adalah

Pembahasan

Kita coba dengan mensubstitusikan nilai ke ,sehingga Berdasarkan perhitungan, didapat hasil adalah dalam bentuk tak tentu. Untuk menyelesaikan soal tersebut, kita bisa coba dengan memanipulasi soal/pernyataan yang diberikan. Setelah kita manipulasi dan dapat bentuk yang sederhana, kita substitusikan nilai . Jadi, nilai dari adalah .

Kita coba dengan mensubstitusikan nilai ke $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 12 of open parentheses fraction numerator square root of x minus square root of 12 over denominator square root of 2 x plus 1 end root minus 5 end fraction close parentheses end cell end table end style$ , sehingga

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Berdasarkan perhitungan, didapat hasil adalah dalam bentuk tak tentu.

Untuk menyelesaikan soal tersebut, kita bisa coba dengan memanipulasi soal/pernyataan yang diberikan.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 12 of open parentheses fraction numerator square root of x minus square root of 12 over denominator square root of 2 x plus 1 end root minus 5 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 12 of open parentheses fraction numerator square root of x minus square root of 12 over denominator square root of 2 x plus 1 end root minus 5 end fraction cross times fraction numerator square root of 2 x plus 1 end root plus 5 over denominator square root of 2 x plus 1 end root plus 5 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 12 of open parentheses fraction numerator open parentheses square root of x minus square root of 12 close parentheses open parentheses square root of 2 x plus 1 end root plus 5 close parentheses over denominator open parentheses square root of 2 x plus 1 end root close parentheses squared minus 5 squared end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 12 of open parentheses fraction numerator open parentheses square root of x minus square root of 12 close parentheses open parentheses square root of 2 x plus 1 end root plus 5 close parentheses over denominator 2 x plus 1 minus 25 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 12 of open parentheses fraction numerator open parentheses square root of x minus square root of 12 close parentheses open parentheses square root of 2 x plus 1 end root plus 5 close parentheses over denominator 2 x minus 24 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 12 of open parentheses fraction numerator open parentheses square root of x minus square root of 12 close parentheses open parentheses square root of 2 x plus 1 end root plus 5 close parentheses over denominator 2 open parentheses x minus 12 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 12 of open parentheses fraction numerator open parentheses square root of x minus square root of 12 close parentheses open parentheses square root of 2 x plus 1 end root plus 5 close parentheses over denominator 2 open parentheses open parentheses square root of x minus square root of 12 close parentheses open parentheses square root of x plus square root of 12 close parentheses close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 12 of open parentheses fraction numerator open parentheses up diagonal strike square root of x minus square root of 12 end strike close parentheses open parentheses square root of 2 x plus 1 end root plus 5 close parentheses over denominator 2 open parentheses open parentheses up diagonal strike square root of x minus square root of 12 end strike close parentheses open parentheses square root of x plus square root of 12 close parentheses close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 12 of open parentheses fraction numerator square root of 2 x plus 1 end root plus 5 over denominator 2 open parentheses square root of x plus square root of 12 close parentheses end fraction close parentheses end cell end table end style$

Setelah kita manipulasi dan dapat bentuk yang sederhana, kita substitusikan nilai .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 12 of open parentheses fraction numerator square root of x minus square root of 12 over denominator square root of 2 x plus 1 end root minus 5 end fraction close parentheses end cell equals cell limit as x rightwards arrow 12 of open parentheses fraction numerator square root of 2 x plus 1 end root plus 5 over denominator 2 open parentheses square root of x plus square root of 12 close parentheses end fraction close parentheses end cell row blank equals cell fraction numerator square root of 2 left parenthesis 12 right parenthesis plus 1 end root plus 5 over denominator 2 open parentheses square root of 12 plus square root of 12 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 25 plus 5 over denominator 2 open parentheses 2 square root of 12 close parentheses end fraction end cell row blank equals cell fraction numerator 5 plus 5 over denominator 4 square root of 12 end fraction end cell row blank equals cell fraction numerator 10 over denominator 4 square root of 12 end fraction cross times fraction numerator square root of 12 over denominator square root of 12 end fraction end cell row blank equals cell fraction numerator 10 square root of 12 over denominator 4 times 12 end fraction end cell row blank equals cell fraction numerator 10 times 2 square root of 3 over denominator 48 end fraction end cell row blank equals cell fraction numerator 20 square root of 3 over denominator 48 end fraction end cell row blank equals cell fraction numerator 5 square root of 3 over denominator 12 end fraction end cell row blank equals cell 5 over 12 square root of 3 end cell end table end style$

Jadi, nilai dari $begin mathsize 14px style stack bold l bold i bold m with bold x bold rightwards arrow bold 12 below bold space fraction numerator square root of bold x bold minus square root of bold 12 over denominator square root of bold 2 bold x bold plus bold 1 end root bold minus bold 5 end fraction end style$ adalah . undefined