Roboguru

Pertanyaan

limit as x rightwards arrow 3 of fraction numerator 9 minus x squared over denominator 4 minus square root of x squared plus 7 end root end fraction equals space...

Pembahasan Soal:

Substitusi nilai x equals 3, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator 9 minus x squared over denominator 4 minus square root of x squared plus 7 end root end fraction end cell equals cell fraction numerator 9 minus open parentheses 3 close parentheses squared over denominator 4 minus square root of open parentheses 3 close parentheses squared plus 7 end root end fraction end cell row blank equals cell fraction numerator 9 minus 9 over denominator 4 minus square root of 16 end fraction end cell row blank equals cell 0 over 0 end cell end table 

Hasilnya bentuk tak tentu, maka limit tersebut dapat diselesaikan dengan metode perkalian akar sekawan berikut ini 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator 9 minus x squared over denominator 4 minus square root of x squared plus 7 end root end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator 9 minus x squared over denominator 4 minus square root of x squared plus 7 end root end fraction cross times fraction numerator 4 plus square root of x squared plus 7 end root over denominator 4 plus square root of x squared plus 7 end root end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses 9 minus x squared close parentheses open parentheses 4 plus square root of x squared plus 7 end root close parentheses over denominator open parentheses 4 minus square root of x squared plus 7 end root close parentheses open parentheses 4 plus square root of x squared plus 7 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses 9 minus x squared close parentheses open parentheses 4 plus square root of x squared plus 7 end root close parentheses over denominator 16 minus open parentheses x squared plus 7 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses 9 minus x squared close parentheses open parentheses 4 plus square root of x squared plus 7 end root close parentheses over denominator open parentheses 9 minus x squared close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of open parentheses 4 plus square root of x squared plus 7 end root close parentheses end cell row blank equals cell 4 plus square root of open parentheses 3 close parentheses squared plus 7 end root end cell row blank equals cell 4 plus square root of 16 end cell row blank equals cell 4 plus 4 end cell row blank equals 8 end table 

Jadi, limit as x rightwards arrow 3 of fraction numerator 9 minus x squared over denominator 4 minus square root of x squared plus 7 end root end fraction equals 8

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Mei 2021

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