Bank Soal Matematika Peminatan SMA Nilai Limit Fungsi Trigonometri

Soal

Pilihan Ganda

Nilai dari limx1 (x21)tan(6x6)sin2(x1)=....\lim\limits_{x\rightarrow1}\ \frac{\left(x^2-1\right)\tan\left(6x-6\right)}{\sin^2\left(x-1\right)}=....

A

44

B

33

C

66

D

1010

E

1212

Pembahasan:

Subtitusi x=1x=1 menghasilkan nilai tak tentu 00\frac{0}{0}

Ingat bahwa

limx0 axsinbx=ab\lim\limits_{x\rightarrow0}\ \frac{ax}{\sin bx}=\frac{a}{b}

limx0 tanaxsinbx=ab\lim\limits_{x\rightarrow0}\ \frac{\tan ax}{\sin bx}=\frac{a}{b}

Bentuk (x21)\left(x^2-1\right) dapat difaktorkan menjadi x21=(x1)(x+1)x^2-1=\left(x-1\right)\left(x+1\right) , maka

limx1 (x21)tan(6x6)sin2(x1)=limx1 (x1)(x+1)tan6(x1)sin2(x1)\lim\limits_{x\rightarrow1}\ \frac{\left(x^2-1\right)\tan\left(6x-6\right)}{\sin^2\left(x-1\right)}=\lim\limits_{x\rightarrow1}\ \frac{\left(x-1\right)\left(x+1\right)\tan6\left(x-1\right)}{\sin^2\left(x-1\right)}

=limx1 ((x1)sin(x1)(x+1)tan6(x1)sin(x1))=\lim\limits_{x\rightarrow1}\ \left(\frac{\left(x-1\right)}{\sin\left(x-1\right)}\cdot\left(x+1\right)\cdot\frac{\tan6\left(x-1\right)}{\sin\left(x-1\right)}\right)

=limx1 (x1)sin(x1)limx1 (x+1)limx1 tan6(x1)sin(x1)=\lim\limits_{x\rightarrow1}\ \frac{\left(x-1\right)}{\sin\left(x-1\right)}\cdot\lim\limits_{x\rightarrow1}\ \left(x+1\right)\cdot\lim\limits_{x\rightarrow1}\ \frac{\tan6\left(x-1\right)}{\sin\left(x-1\right)}

=1limx1 (x+1)6=1\cdot\lim\limits_{x\rightarrow1}\ \left(x+1\right)\cdot6

=1(1+1)6=1\cdot\left(1+1\right)\cdot6

=12=12

Jadi, nilai dari limx1 (x21)tan(6x6)sin2(x1)=12\lim\limits_{x\rightarrow1}\ \frac{\left(x^2-1\right)\tan\left(6x-6\right)}{\sin^2\left(x-1\right)}=12

K13 Kelas XII Matematika Peminatan Trigonometri Limit Fungsi Trigonometri Nilai Limit Fungsi Trigonometri Skor 3
Teknik Hitung LOTS
Video
19 April 2022
Nilai Limit Fungsi Trigonometri
Rangkuman

Siswa

Ingin latihan soal, nonton, atau unduh materi belajar lebih banyak?

Buat Akun Gratis

Guru

Ingin akses bank soal, nonton, atau unduh materi belajar lebih banyak?

Buat Akun Gratis

Soal Populer Hari Ini

Cek Contoh Kuis Online

Kejar Kuis

Cek Contoh Bank Soal

Kejar Soal