Pertanyaan

Tentukan limit dari fungsi berikut! b. x → 5 lim x + 5 + 2 x + 1 2 x + 1

Tentukan limit dari fungsi berikut!

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

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Habis dalam

Klaim

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

$begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator 2 x plus 1 over denominator square root of x plus 5 end root plus square root of 2 x plus 1 end root end fraction equals square root of 11 minus square root of 10 end style$ .

Pembahasan

Jadi .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 5 of fraction numerator 2 x plus 1 over denominator square root of x plus 5 end root plus square root of 2 x plus 1 end root end fraction end cell equals cell fraction numerator 2 open parentheses 5 close parentheses plus 1 over denominator square root of 5 plus 5 end root plus square root of 2 open parentheses 5 close parentheses plus 1 end root end fraction end cell row blank equals cell fraction numerator 10 plus 1 over denominator square root of 10 plus square root of 11 end fraction end cell row blank equals cell fraction numerator 11 over denominator square root of 10 plus square root of 11 end fraction cross times fraction numerator square root of 10 minus square root of 11 over denominator square root of 10 minus square root of 11 end fraction end cell row blank equals cell fraction numerator 11 open parentheses square root of 10 minus square root of 11 close parentheses over denominator 10 minus 11 end fraction end cell row blank equals cell fraction numerator 11 open parentheses square root of 10 minus square root of 11 close parentheses over denominator negative 1 end fraction end cell row blank equals cell negative 1 open parentheses square root of 10 minus square root of 11 close parentheses end cell row blank equals cell square root of 11 minus square root of 10 end cell row blank blank blank end table end style$

Jadi $begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator 2 x plus 1 over denominator square root of x plus 5 end root plus square root of 2 x plus 1 end root end fraction equals square root of 11 minus square root of 10 end style$ .