Pertanyaan

Tentukan nilai limit berikut. x → 0 lim 2 x 8 + x − 8 − 3 x

Tentukan nilai limit berikut.

$x \to 0 lim \frac{8 + x - 8 - 3 x}{2 x}$

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

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Pembahasan

Mencari nilai limit: Jadi, .

Mencari nilai limit:

$limit as x rightwards arrow thin space 0 of open parentheses fraction numerator square root of 8 plus x end root minus square root of 8 minus 3 x end root over denominator 2 x end fraction close parentheses equals 1 half times limit as x rightwards arrow thin space 0 of open parentheses fraction numerator square root of 8 plus x end root minus square root of 8 minus 3 x end root over denominator x end fraction close parentheses equals 1 half times limit as x rightwards arrow thin space 0 of open parentheses fraction numerator square root of 8 plus x end root minus square root of 8 minus 3 x end root cross times fraction numerator square root of 8 plus x end root plus square root of 8 minus 3 x end root over denominator square root of 8 plus x end root plus square root of 8 minus 3 x end root end fraction over denominator x end fraction close parentheses equals 1 half times limit as x rightwards arrow thin space 0 of open parentheses fraction numerator fraction numerator 8 plus x minus 8 plus 3 x over denominator square root of 8 plus x end root plus square root of 8 minus 3 x end root end fraction over denominator x end fraction close parentheses equals 1 half times limit as x rightwards arrow thin space 0 of open parentheses fraction numerator fraction numerator 4 x over denominator square root of 8 plus x end root plus square root of 8 minus 3 x end root end fraction over denominator x end fraction close parentheses equals 1 half times limit as x rightwards arrow thin space 0 of open parentheses fraction numerator 4 over denominator square root of x plus 8 end root plus square root of negative 3 x plus 8 end root end fraction close parentheses equals 1 half times fraction numerator 4 over denominator square root of 0 plus 8 end root plus square root of negative 3 times thin space 0 plus 8 end root end fraction equals 1 half times fraction numerator 4 over denominator square root of 8 plus square root of 8 end fraction equals 1 half times fraction numerator 4 over denominator 2 square root of 2 plus 2 square root of 2 end fraction equals 1 half times fraction numerator 4 over denominator 4 square root of 2 end fraction equals 1 half times fraction numerator 1 over denominator square root of 2 end fraction equals fraction numerator 1 over denominator 2 square root of 2 end fraction$

Jadi, $limit as x rightwards arrow thin space 0 of open parentheses fraction numerator square root of 8 plus x end root minus square root of 8 minus 3 x end root over denominator 2 x end fraction close parentheses equals fraction numerator 1 over denominator 2 square root of 2 end fraction$ .