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Nilai dari  = ....

Nilai dari limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator 1 minus square root of x minus 3 end root end fraction = ....

  1. 32

  2. 16

  3. negative 4

  4. negative 16

  5. 4

Jawaban:

Dengan menggunakan sifat penyelesaian limit dengan perkalian sekawan, maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator 1 minus square root of x minus 3 end root end fraction cross times fraction numerator 1 plus square root of x minus 3 end root over denominator 1 plus square root of x minus 3 end root end fraction end cell equals cell limit as x rightwards arrow 4 of fraction numerator open parentheses x squared minus 16 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator 1 squared minus open parentheses square root of x minus 3 end root close parentheses squared end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator open parentheses x squared minus 16 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator 1 minus open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator open parentheses x minus 4 close parentheses open parentheses x plus 4 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator 1 minus x plus 3 end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator open parentheses x minus 4 close parentheses open parentheses x plus 4 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator 4 minus x end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator up diagonal strike open parentheses x minus 4 close parentheses end strike open parentheses x plus 4 close parentheses cross times open parentheses 1 plus square root of x minus 3 end root close parentheses over denominator negative up diagonal strike left parenthesis x minus 4 right parenthesis end strike end fraction end cell row blank equals cell limit as x rightwards arrow 4 of open parentheses negative left parenthesis x plus 4 right parenthesis cross times open parentheses 1 plus square root of x minus 3 end root close parentheses close parentheses end cell row blank equals cell negative left parenthesis 4 plus 4 right parenthesis cross times open parentheses 1 plus square root of 4 minus 3 end root close parentheses end cell row blank equals cell negative 8 cross times 2 end cell row blank equals cell negative 16 end cell end table

Maka, nilai dari limit as x rightwards arrow 4 of fraction numerator x squared minus 16 over denominator 1 minus square root of x minus 3 end root end fraction adalah negative 16

Oleh karena itu, jawaban yang benar adalah D

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