Pertanyaan

HItunglah nilai limit fungsi-fungsi berikut. x → 1 lim 2 − x + 3 1 − x 2

HItunglah nilai limit fungsi-fungsi berikut.

$x \to 1 lim \frac{1 - x ^{2}}{2 - x + 3}$

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

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

Pembahasan

Substitusi nilai , diperoleh Hasilnya bentuk tak tentu, maka limit tersebut dapat diselesaikan dengan cara mengalikan akar sekawan seperti di bawah ini Jadi, .

Substitusi nilai x equals 1 , diperoleh

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