Nilai dari x→∞lim​2x+15x2+3x−2​ adalah ....

Pertanyaan

Nilai dari limit as x rightwards arrow infinity of fraction numerator 5 x squared plus 3 x minus 2 over denominator 2 x plus 1 end fraction spaceadalah ....

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari limit as x rightwards arrow infinity of fraction numerator 5 x squared plus 3 x minus 2 over denominator 2 x plus 1 end fraction spaceadalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell infinity. end cell end table

Pembahasan

Diketahui limit tak hingga limit as x rightwards arrow infinity of fraction numerator 5 x squared plus 3 x minus 2 over denominator 2 x plus 1 end fraction comma dengan f open parentheses x close parentheses equals 5 x squared plus 3 x minus 2 space text dan end text space g open parentheses x close parentheses equals 2 x plus 1 maka nilai dari limit as x rightwards arrow infinity of fraction numerator 5 x squared plus 3 x minus 2 over denominator 2 x plus 1 end fraction spaceyaitu dengan membagi setiap fungsi f open parentheses x close parentheses space text dan end text space g open parentheses x close parentheses spacedengan variabel pangkat tertinggi open parentheses x squared close parentheses sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 5 x squared plus 3 x minus 2 over denominator 2 x plus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 5 x squared over denominator x end fraction end style plus begin display style fraction numerator 3 x over denominator x end fraction end style minus begin display style 2 over x end style over denominator begin display style fraction numerator 2 x over denominator x end fraction end style plus begin display style 1 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 5 x plus 3 minus 2 over x end style over denominator begin display style 2 plus 1 over x end style end fraction end cell end table

ingat bahwa limit as x rightwards arrow infinity of a over x to the power of n equals 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator begin display style 5 x plus 3 minus 2 over x end style over denominator begin display style 2 plus 1 over x end style end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 5 x plus 3 minus 0 end style over denominator begin display style 2 plus 0 end style end fraction end cell row blank equals cell fraction numerator 5 times infinity plus 3 over denominator 2 end fraction end cell row blank equals infinity end table

 


Jadi nilai dari limit as x rightwards arrow infinity of fraction numerator 5 x squared plus 3 x minus 2 over denominator 2 x plus 1 end fraction spaceadalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell infinity. end cell end table

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