Roboguru

HItunglah nilai limit fungsi-fungsi berikut.

Pertanyaan

HItunglah nilai limit fungsi-fungsi berikut. 

  • limit as x rightwards arrow 1 of fraction numerator 1 minus x squared over denominator 2 minus square root of x plus 3 end root end fraction  

Pembahasan Soal:

Substitusi nilai x equals 1, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator 1 minus x squared over denominator 2 minus square root of x plus 3 end root end fraction end cell equals cell fraction numerator 1 minus open parentheses 1 close parentheses squared over denominator 2 minus square root of open parentheses 1 close parentheses plus 3 end root end fraction end cell row blank equals cell fraction numerator 1 minus 1 over denominator 2 minus 2 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 cara mengalikan akar sekawan seperti di bawah ini 

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

Jadi, limit as x rightwards arrow 1 of fraction numerator 1 minus x squared over denominator 2 minus square root of x plus 3 end root end fraction equals 8

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Mei 2021

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