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Pertanyaan

limit as x rightwards arrow infinity of space square root of x squared minus 3 end root minus square root of x squared plus 2 x minus 3 end root equals....

Pembahasan Soal:

Gunakan konsep limit tak hingga bentuk akar.

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root close parentheses equals open curly brackets table attributes columnalign left end attributes row cell infinity comma space a greater than p end cell row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space a equals p end cell row cell negative infinity comma space a less than p end cell end table close end style 

Berdasarkan konsep limit tak hingga bentuk akar limit pada soal memenuhi syarat a equals p, sehingga dapat dihitung sebagai berikut.

table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses square root of x squared minus 3 end root minus square root of x squared plus 2 x minus 3 end root close parentheses end cell row blank equals cell fraction numerator b minus q over denominator 2 square root of a end fraction equals fraction numerator 0 minus 2 over denominator 2 square root of 1 end fraction end cell row blank equals cell fraction numerator negative 2 over denominator 2 end fraction end cell row blank equals cell negative 1 end cell end table

Jadi, diperoleh nilainya adalah limit as x rightwards arrow infinity of space square root of x squared minus 3 end root minus square root of x squared plus 2 x minus 3 end root equals negative 1

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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