Pertanyaan

x → 3 lim x − 3 sin ( x + 1 − 2 ) = ...

$x \to 3 lim \frac{sin ( x + 1 - 2 )}{x - 3} = ...$

-1
0

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Habis dalam

Klaim

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Misalkan Jika x = 3 maka y = 2 Sehingga, Misalkan z = y - 2 maka y = z + 2 maka :

Misalkan
Jika x = 3 maka y = 2
Sehingga,

$limit as x rightwards arrow 3 of fraction numerator sin open parentheses square root of x plus 1 end root minus 2 close parentheses over denominator x minus 3 end fraction equals limit as y rightwards arrow 2 of fraction numerator sin begin display style open parentheses y minus 2 close parentheses end style over denominator y squared minus 1 minus 3 end fraction equals limit as y rightwards arrow 2 of fraction numerator sin open parentheses y minus 2 close parentheses over denominator y squared minus 4 end fraction equals limit as y rightwards arrow 2 of fraction numerator sin open parentheses y minus 2 close parentheses over denominator open parentheses y minus 2 close parentheses open parentheses y plus 2 close parentheses end fraction$

Misalkan z = y - 2 maka y = z + 2 maka :

$limit as y minus 2 rightwards arrow of fraction numerator sin open parentheses z plus 2 minus 2 close parentheses over denominator open parentheses z plus 2 minus 2 close parentheses open parentheses z plus 2 plus 2 close parentheses end fraction limit as z rightwards arrow 0 of fraction numerator sin begin display style space end style begin display style z end style over denominator open parentheses z plus 4 close parentheses end fraction equals 1 fourth$