Pertanyaan

Nilai dari x → π lim π + tanx − π − tanx sinx adalah....

Nilai dari $x \to π lim \frac{sinx}{π + tanx - π - tanx}$ adalah ....

8 dari 10 siswa nilainya naik

dengan paket belajar pilihan

Habis dalam

Klaim

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan perhitungan berikut! Dengan demikian, nilai dari adalah . Jadi, jawaban yang tepat adalah B.

Perhatikan perhitungan berikut!

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow straight pi of invisible function application fraction numerator sin invisible function application straight x over denominator square root of straight pi plus tan invisible function application straight x end root minus square root of straight pi minus tan invisible function application straight x end root end fraction end cell row blank equals cell limit as straight x rightwards arrow straight pi of open parentheses fraction numerator sin invisible function application straight x over denominator square root of straight pi plus tan invisible function application straight x end root minus square root of straight pi minus tan invisible function application straight x end root end fraction times fraction numerator square root of straight pi plus tan invisible function application straight x end root plus square root of straight pi minus tan invisible function application straight x end root over denominator square root of straight pi plus tan invisible function application straight x end root plus square root of straight pi minus tan invisible function application straight x end root end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow straight pi of fraction numerator sinx open parentheses square root of straight pi plus tanx end root plus square root of straight pi minus tanx end root close parentheses over denominator left parenthesis straight pi plus tanx right parenthesis minus left parenthesis straight pi minus tanx right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow straight pi of fraction numerator sinx open parentheses square root of straight pi plus tanx end root plus square root of straight pi minus tanx end root close parentheses over denominator 2 tanx end fraction end cell row blank equals cell limit as straight x rightwards arrow straight pi of fraction numerator sinx open parentheses square root of straight pi plus tanx end root plus square root of straight pi minus tanx end root close parentheses over denominator 2 sinx over cosx end fraction end cell row blank equals cell limit as straight x rightwards arrow straight pi of open parentheses cosx over 2 open parentheses square root of straight pi plus tanx end root plus square root of straight pi minus tanx end root close parentheses close parentheses end cell row blank equals cell cosπ over 2 open parentheses square root of straight pi plus tanπ end root plus square root of straight pi minus tanπ end root close parentheses end cell row blank equals cell fraction numerator negative 1 over denominator 2 end fraction open parentheses square root of straight pi plus 0 end root plus square root of straight pi minus 0 end root close parentheses end cell row blank equals cell negative 1 half open parentheses square root of straight pi plus square root of straight pi close parentheses end cell row blank equals cell negative 1 half open parentheses 2 square root of straight pi close parentheses end cell row blank equals cell negative square root of straight pi end cell end table end style$

Dengan demikian, nilai dari $begin mathsize 14px style limit as straight x rightwards arrow straight pi of fraction numerator sinx over denominator square root of straight pi plus tanx end root minus square root of straight pi minus tanx end root end fraction end style$ adalah .

Jadi, jawaban yang tepat adalah B.