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Pertanyaan

Diketahui fungsi f dan g dinyatakan oleh f left parenthesis x right parenthesis equals 9 x squared plus 2 x minus 5 dan g left parenthesis x right parenthesis equals 9 x squared minus 4 x plus 3. Tentukan nilai limit as x rightwards arrow infinity of open parentheses square root of f open parentheses x close parentheses end root minus square root of g open parentheses x close parentheses end root close parentheses !

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

hasil dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses square root of 9 x squared plus 2 x minus 5 end root minus square root of 9 x squared minus 4 x plus 3 end root close parentheses end cell end table adalah 1.

Pembahasan

Ingatlah rumus cepat untuk menghitung limit tak hingga.

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 untuk 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 untuk space a equals p minus infinity comma space untuk space a less than p end cell end table close

Pertama-tama, gunakan metode substitusi untuk mencari limit pada soal

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of f open parentheses x close parentheses end root minus square root of g open parentheses x close parentheses end root close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses square root of 9 x squared plus 2 x minus 5 end root minus square root of 9 x squared minus 4 x plus 3 end root close parentheses end cell row blank equals cell infinity minus infinity end cell end table

Limit menghasilkan bentuk tak tentu, maka gunakan rumus cepat limit tak hingga.

Karena koefisien x squared akar yang dikurangi dengan pengurang sama, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of 9 x squared plus 2 x minus 5 end root minus square root of 9 x squared minus 4 x plus 3 end root close parentheses end cell equals cell fraction numerator 2 minus open parentheses negative 4 close parentheses over denominator 2 square root of 9 end fraction end cell row blank equals cell fraction numerator 2 plus 4 over denominator 2 open parentheses 3 close parentheses end fraction end cell row blank equals cell 6 over 6 end cell row blank equals 1 end table  

Dengan demikian, hasil dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses square root of 9 x squared plus 2 x minus 5 end root minus square root of 9 x squared minus 4 x plus 3 end root close parentheses end cell end table adalah 1.

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