Roboguru

Nilai  adalah ....

Pertanyaan

Nilai limit as x rightwards arrow 1 of space fraction numerator 9 square root of x minus 9 over denominator x minus 1 end fraction adalah ....

Pembahasan Soal:

Perhatikan perhitungan berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of space fraction numerator 9 square root of x minus 9 over denominator x minus 1 end fraction end cell equals cell fraction numerator 9 square root of 1 minus 9 over denominator 1 minus 1 end fraction end cell row blank equals cell fraction numerator 9 minus 9 over denominator 1 minus 1 end fraction end cell row blank equals cell 0 over 0 end cell end table 

Karena hasil dari limit tersebut ketika disubstitusikan x equals 1 merupakan bilangan tak tentu 0 over 0, maka kita kalikan bentuk limit tersebut dengan akar sekawan.
Dengan demikian, diperoleh hasil perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell limit as x rightwards arrow 1 of space fraction numerator 9 square root of x minus 9 over denominator x minus 1 end fraction end cell equals cell limit as x rightwards arrow 1 of space open parentheses fraction numerator 9 square root of x minus 9 over denominator x minus 1 end fraction cross times fraction numerator 9 square root of x plus 9 over denominator 9 square root of x plus 9 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 1 of space open parentheses fraction numerator 81 x minus 81 over denominator open parentheses x minus 1 close parentheses open parentheses 9 square root of x plus 9 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 1 of space open parentheses fraction numerator 81 up diagonal strike left parenthesis x minus 1 right parenthesis end strike over denominator up diagonal strike open parentheses x minus 1 close parentheses end strike open parentheses 9 square root of x plus 9 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 1 of space open parentheses fraction numerator 81 over denominator 9 square root of x plus 9 end fraction close parentheses end cell row blank equals cell fraction numerator 81 over denominator 9 square root of 1 plus 9 end fraction end cell row blank equals cell 81 over 18 end cell row blank equals cell 4 1 half end cell end table

Jadi, diperoleh bahwa limit as x rightwards arrow 1 of space fraction numerator 9 square root of x minus 9 over denominator x minus 1 end fraction equals 4 1 half.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Agustus 2021

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