Pertanyaan

Nilai dari l i m x → 0 ( 2 x + 9 − 3 x + 9 3 x + 4 − x + 4 ) adalah ....

Nilai dari $l i m_{x \to 0} (\frac{3 x + 4 - x + 4}{2 x + 9 - 3 x + 9})$ adalah ....

-3
-1
1
3
5

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A. Nadhira

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Limit fungsi tersebut menghasilkan bentuk tak tentu, sehingga kita perlu mengalikannya dengan akar sekawanterlebih dahulu.

$begin mathsize 14px style l i m subscript x rightwards arrow 0 space end subscript open parentheses fraction numerator square root of 3 x plus 4 end root space minus space square root of x plus 4 end root over denominator square root of 2 x plus 9 end root minus space square root of 3 x plus 9 end root end fraction close parentheses equals 0 over 0 end style$

Limit fungsi tersebut menghasilkan bentuk tak tentu, sehingga kita perlu mengalikannya dengan akar sekawan terlebih dahulu.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack l i m subscript space with x rightwards arrow 0 below open parentheses fraction numerator square root of 3 x plus 4 end root space minus space square root of x plus 4 end root over denominator square root of 2 x plus 9 end root minus space square root of 3 x plus 9 end root end fraction close parentheses end cell row blank equals cell stack l i m subscript space with x rightwards arrow 0 below open parentheses fraction numerator square root of 3 x plus 4 end root space minus space square root of x plus 4 end root over denominator square root of 2 x plus 9 end root minus space square root of 3 x plus 9 end root end fraction close parentheses cross times open parentheses fraction numerator square root of 3 x plus 4 end root space plus space square root of x plus 4 end root over denominator square root of 3 x plus 4 end root space plus space square root of x plus 4 end root end fraction close parentheses end cell row blank blank cell space space space space space space cross times open parentheses fraction numerator square root of 2 x plus 9 end root plus space square root of 3 x plus 9 end root over denominator square root of 2 x plus 9 end root plus space square root of 3 x plus 9 end root end fraction close parentheses end cell row blank equals cell stack l i m subscript space with x rightwards arrow 0 below fraction numerator left parenthesis 3 x plus 4 right parenthesis minus left parenthesis x plus 4 right parenthesis over denominator left parenthesis 2 x plus 9 right parenthesis minus left parenthesis 3 x plus 9 right parenthesis end fraction cross times open parentheses fraction numerator square root of 2 x plus 9 end root plus space square root of 3 x plus 9 end root over denominator square root of 3 x plus 4 end root space plus space square root of x plus 4 end root end fraction close parentheses end cell row blank equals cell stack l i m subscript space with x rightwards arrow 0 below fraction numerator 2 x over denominator negative x end fraction open parentheses fraction numerator square root of 2 x plus 9 end root plus space square root of 3 x plus 9 end root over denominator square root of 3 x plus 4 end root space plus space square root of x plus 4 end root end fraction close parentheses end cell row blank equals cell stack l i m subscript space with x rightwards arrow 0 below minus 2 open parentheses fraction numerator square root of 2 x plus 9 end root plus space square root of 3 x plus 9 end root over denominator square root of 3 x plus 4 end root space plus space square root of x plus 4 end root end fraction close parentheses end cell row blank equals cell negative 2 open parentheses fraction numerator square root of 2.0 plus 9 end root plus space square root of 3.0 plus 9 end root over denominator square root of 3.0 plus 4 end root space plus space square root of 0 plus 4 end root end fraction close parentheses end cell row blank equals cell negative 2 open parentheses 6 over 4 close parentheses equals negative 3 end cell end table$