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x → ∞ lim ​ x − 6 3 x − 2 ​ − 2 x + 4 ​ ​ = ...

            

N. Puspita

Master Teacher

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hasil limitnya adalah 0.

hasil limitnya adalah 0.

Pembahasan

Pembahasan

Ingat: . Jadi, hasil limitnya adalah 0.

Ingat: limit as x rightwards arrow infinity of k over x to the power of n equals k over infinity to the power of n equals 0.

 table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction cross times fraction numerator begin display style 1 over x end style over denominator begin display style 1 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator square root of begin display style fraction numerator 3 x over denominator x squared end fraction end style minus begin display style 2 over x squared end style end root minus square root of begin display style fraction numerator 2 x over denominator x squared end fraction end style plus begin display style 4 over x squared end style end root over denominator begin display style x over x end style minus begin display style 6 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator square root of begin display style 3 over x minus 2 over x squared end style end root minus square root of begin display style 2 over x plus 4 over x squared end style end root over denominator begin display style 1 minus 6 over x end style end fraction end cell row blank equals cell fraction numerator square root of begin display style 3 over infinity minus 2 over infinity squared end style end root minus square root of begin display style 2 over infinity plus 4 over infinity squared end style end root over denominator begin display style 1 minus 6 over infinity end style end fraction end cell row blank equals cell space fraction numerator square root of begin display style 0 minus 0 end style end root minus square root of begin display style 0 plus 0 end style end root over denominator begin display style 1 minus 0 end style end fraction end cell row blank equals cell 0 over 1 end cell row blank equals 0 end table 

Jadi, hasil limitnya adalah 0.

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