Pertanyaan

Hitunglah: b. x → 2 lim 5 x − 1 − 4 x + 1 x + 2 − 3 x − 2

Hitunglah:

b. $x \to 2 lim \frac{x + 2 - 3 x - 2}{5 x - 1 - 4 x + 1}$

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Habis dalam

Klaim

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Jawaban

nilai limit tersebut adalah .

nilai limit tersebut adalah negative 3

Pembahasan

Pertama kita coba dengan cara mensubstitusi: Karena menghasilkan yaitu suatu bentuk tak tentu, maka kita coba menggunakan cara mengalikan dengan akar sekawan: Jadi, nilai limit tersebut adalah .

Pertama kita coba dengan cara mensubstitusi:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator square root of x plus 2 end root minus square root of 3 x minus 2 end root over denominator square root of 5 x minus 1 end root minus square root of 4 x plus 1 end root end fraction end cell equals cell fraction numerator square root of 2 plus 2 end root minus square root of 3 left parenthesis 2 right parenthesis minus 2 end root over denominator square root of 5 left parenthesis 2 right parenthesis minus 1 end root minus square root of 4 left parenthesis 2 right parenthesis plus 1 end root end fraction end cell row blank equals cell fraction numerator square root of 4 minus square root of 6 minus 2 end root over denominator square root of 10 minus 1 end root minus square root of 8 plus 1 end root end fraction end cell row blank equals cell fraction numerator 2 minus square root of 4 over denominator square root of 9 minus square root of 9 end fraction end cell row blank equals cell fraction numerator 2 minus 2 over denominator 3 minus 3 end fraction end cell row blank equals cell 0 over 0 end cell end table$

Karena menghasilkan 0 over 0 yaitu suatu bentuk tak tentu, maka kita coba menggunakan cara mengalikan dengan akar sekawan:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 2 of fraction numerator square root of x plus 2 end root minus square root of 3 x minus 2 end root over denominator square root of 5 x minus 1 end root minus square root of 4 x plus 1 end root end fraction end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator square root of x plus 2 end root minus square root of 3 x minus 2 end root over denominator square root of 5 x minus 1 end root minus square root of 4 x plus 1 end root end fraction cross times fraction numerator square root of 5 x minus 1 end root plus square root of 4 x plus 1 end root over denominator square root of 5 x minus 1 end root plus square root of 4 x plus 1 end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator square root of open parentheses x plus 2 close parentheses open parentheses 5 x minus 1 close parentheses end root minus square root of open parentheses 3 x minus 2 close parentheses open parentheses 5 x minus 1 close parentheses end root plus square root of open parentheses x plus 2 close parentheses open parentheses 4 x plus 1 close parentheses end root minus square root of open parentheses 3 x minus 2 close parentheses open parentheses 4 x plus 1 close parentheses end root over denominator open parentheses 5 x minus 1 close parentheses minus open parentheses 4 x plus 1 close parentheses end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 2 of open parentheses fraction numerator square root of 5 x squared plus 9 x minus 2 end root minus square root of 15 x squared minus 13 x plus 2 end root plus square root of 4 x squared plus 9 x plus 2 end root minus square root of 12 x squared minus 5 x minus 2 end root over denominator x end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator square root of 5 left parenthesis 2 right parenthesis squared plus 9 left parenthesis 2 right parenthesis minus 2 end root minus square root of 15 left parenthesis 2 right parenthesis squared minus 13 left parenthesis 2 right parenthesis plus 2 end root plus square root of 4 left parenthesis 2 right parenthesis squared plus 9 left parenthesis 2 right parenthesis plus 2 end root minus square root of 12 left parenthesis 2 right parenthesis squared minus 5 left parenthesis 2 right parenthesis minus 2 end root over denominator 2 end fraction close parentheses end cell row blank equals cell fraction numerator square root of 0 minus square root of 36 plus square root of 36 minus square root of 36 over denominator 2 end fraction end cell row blank equals cell fraction numerator negative square root of 36 over denominator 2 end fraction end cell row blank equals cell fraction numerator negative 6 over denominator 2 end fraction end cell row blank equals cell negative 3 end cell end table end style$

Jadi, nilai limit tersebut adalah negative 3 .