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Tentukan nilai dari x → − 2 lim ​ x + 2 2 x + 13 ​ − x + 11 ​ ​ .

Tentukan nilai dari .

  1. undefined 

  2. undefined 

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begin mathsize 14px style limit as x rightwards arrow negative 2 of fraction numerator square root of 2 x plus 13 end root minus square root of x plus 11 end root over denominator x plus 2 end fraction equals 1 over 6 end style 

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Substitusi Karena bentuk tak tentu, maka dikali akar sekawan dahulu Jadi ,

Substitusi begin mathsize 14px style x equals negative 2 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow negative 2 of fraction numerator square root of 2 x plus 13 end root minus square root of x plus 11 end root over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator square root of 2 times left parenthesis negative 2 right parenthesis plus 13 end root minus square root of negative 2 plus 11 end root over denominator negative 2 plus 2 end fraction end cell row blank equals cell fraction numerator square root of 9 minus square root of 9 over denominator 0 end fraction end cell row blank equals cell 0 over 0 end cell end table end style  

Karena begin mathsize 14px style 0 over 0 end style bentuk tak tentu, maka dikali akar sekawan dahulu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow negative 2 of fraction numerator square root of 2 x plus 13 end root minus square root of x plus 11 end root over denominator x plus 2 end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of open parentheses fraction numerator square root of 2 x plus 13 end root minus square root of x plus 11 end root over denominator x plus 2 end fraction times fraction numerator square root of 2 x plus 13 end root plus square root of x plus 11 end root over denominator square root of 2 x plus 13 end root plus square root of x plus 11 end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator 2 x plus 13 minus left parenthesis x plus 11 right parenthesis over denominator left parenthesis x plus 2 right parenthesis left parenthesis square root of 2 x plus 13 end root plus square root of x plus 11 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator 2 x plus 13 minus x minus 11 over denominator left parenthesis x plus 2 right parenthesis left parenthesis square root of 2 x plus 13 end root plus square root of x plus 11 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator x plus 2 over denominator left parenthesis x plus 2 right parenthesis left parenthesis square root of 2 x plus 13 end root plus square root of x plus 11 end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator 1 over denominator square root of 2 x plus 13 end root plus square root of x plus 11 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 2 times left parenthesis negative 2 right parenthesis plus 13 end root plus square root of negative 2 plus 11 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 9 plus square root of 9 end fraction end cell row blank equals cell fraction numerator 1 over denominator 3 plus 3 end fraction end cell row blank equals cell 1 over 6 end cell row blank blank blank end table end style  

 

Jadibegin mathsize 14px style limit as x rightwards arrow negative 2 of fraction numerator square root of 2 x plus 13 end root minus square root of x plus 11 end root over denominator x plus 2 end fraction equals 1 over 6 end style 

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