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Tentukan nilai limit fungsi berikut. x → ∞ lim ​ 4 x 2 + 2 x 2 x 2 + 3 ​

Tentukan nilai limit fungsi berikut.

 

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L. Sibuea

Master Teacher

Mahasiswa/Alumni Universitas Riau

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nilai dari adalah

nilai dari limit as x rightwards arrow infinity of space fraction numerator 2 x squared plus 3 over denominator 4 x squared plus 2 x end fraction adalah 1 half. 

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Pembahasan

Dengan menggunakan aturan limit untuk pembagian buah fungsi, maka nilai adalah Dengan demikian, nilai dari adalah

Dengan menggunakan aturan limit untuk pembagian 2 buah fungsi, maka nilai limit as x rightwards arrow infinity of space fraction numerator 2 x squared plus 3 over denominator 4 x squared plus 2 x end fraction adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator 2 x squared plus 3 over denominator 4 x squared plus 2 x end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 2 x squared over denominator x squared end fraction end style plus begin display style 3 over x squared end style over denominator begin display style fraction numerator 4 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 2 x over denominator x squared end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style 2 plus 3 over x squared end style over denominator begin display style 4 plus 2 over x end style end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow infinity of space 2 plus 3 over x squared space over denominator limit as x rightwards arrow infinity of space 4 plus 2 over x space end fraction end cell row blank equals cell fraction numerator 2 plus 0 over denominator 4 plus 0 end fraction end cell row blank equals cell 2 over 4 end cell row cell limit as x rightwards arrow infinity of space fraction numerator 2 x squared plus 3 over denominator 4 x squared plus 2 x end fraction end cell equals cell 1 half end cell end table 

Dengan demikian, nilai dari limit as x rightwards arrow infinity of space fraction numerator 2 x squared plus 3 over denominator 4 x squared plus 2 x end fraction adalah 1 half. 

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