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x → ∞ lim ​ ( 4 x 2 + 4 x − 3 ​ − ( 2 x − 5 ) ) = ....

   

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N. Puspita

Master Teacher

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 limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 4 x minus 3 end root minus open parentheses 2 x minus 5 close parentheses close parentheses equals 6   

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jika dan hanya jika jika dan hanya jika jika dan hanya jika Maka, hasil limit tersebut: Karena , maka Jadi,

limit as x rightwards arrow infinity of square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root equals straight L 

  • straight L equals negative infinity jika dan hanya jika a less than p 
  • straight L equals infinity jika dan hanya jika a greater than p 
  • straight L equals fraction numerator b minus q over denominator 2 square root of a end fraction jika dan hanya jika a equals p 

Maka, hasil limit tersebut:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 4 x minus 3 end root minus open parentheses 2 x minus 5 close parentheses close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 4 x minus 3 end root minus square root of open parentheses 2 x minus 5 close parentheses squared end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 4 x minus 3 end root minus square root of 4 x squared minus 20 x plus 25 end root close parentheses end cell end table  

Karena a equals p, maka straight L equals fraction numerator b minus q over denominator 2 square root of a end fraction 

table attributes columnalign right center left columnspacing 0px end attributes row straight L equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator 4 minus open parentheses negative 20 close parentheses over denominator 2 square root of 4 end fraction end cell row blank equals cell fraction numerator 24 over denominator 2 times 2 end fraction end cell row blank equals cell 24 over 4 end cell row blank equals 6 end table   

Jadi, limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 4 x minus 3 end root minus open parentheses 2 x minus 5 close parentheses close parentheses equals 6   

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