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Nilai x→∞lim​(4x−2−16x2−2x−5​)= ...

Pertanyaan

Nilai limit as x rightwards arrow infinity of open parentheses 4 x minus 2 minus square root of 16 x squared minus 2 x minus 5 end root close parentheses equals space... 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

 limit as x rightwards arrow infinity of open parentheses 4 x minus 2 minus square root of 16 x squared minus 2 x minus 5 end root close parentheses equals negative 7 over 4

Pembahasan

Bentuk limit tersebut dapat deselesaikan dengan cara perkalian dengan akar sekawan. 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses 4 x minus 2 minus square root of 16 x squared minus 2 x minus 5 end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses 4 x minus 2 minus square root of 16 x squared minus 2 x minus 5 end root close parentheses cross times end cell row blank blank cell fraction numerator open parentheses 4 x minus 2 plus square root of 16 x squared minus 2 x minus 5 end root close parentheses over denominator open parentheses 4 x minus 2 plus square root of 16 x squared minus 2 x minus 5 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 4 x minus 2 close parentheses squared minus open parentheses 16 x squared minus 2 x minus 5 close parentheses over denominator 4 x minus 2 plus square root of 16 x squared minus 2 x minus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator negative 14 x plus 9 over denominator 4 x minus 2 plus square root of 16 x squared minus 2 x minus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator negative 14 x plus 9 over denominator 4 x minus 2 plus square root of 16 x squared minus 2 x minus 5 end root end fraction cross times fraction numerator open parentheses begin display style 1 over x end style close parentheses over denominator open parentheses begin display style 1 over x end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator negative 14 plus begin display style 9 over x end style over denominator 4 minus begin display style 2 over x end style plus square root of begin display style 16 minus 2 over x minus 5 over x squared end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator negative 14 plus begin display style 0 end style over denominator 4 minus 0 plus square root of begin display style 16 minus 0 minus 0 end style end root end fraction end cell row blank equals cell fraction numerator negative 14 over denominator 4 plus 4 end fraction end cell row blank equals cell negative 14 over 8 end cell row blank equals cell negative 7 over 4 end cell row blank blank blank end table 

Jadi, limit as x rightwards arrow infinity of open parentheses 4 x minus 2 minus square root of 16 x squared minus 2 x minus 5 end root close parentheses equals negative 7 over 4

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