Bank Soal Matematika SMA Nilai Limit Fungsi Trigonometri

Soal

Pilgan

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 Trigonometri Limit Fungsi Trigonometri Nilai Limit Fungsi Trigonometri Skor 3
Matematika Peminatan Teknik Hitung LOTS
Video
19 April 2022
Nilai Limit Fungsi Trigonometri | Matematika Peminatan | Kelas XII
Rangkuman
08 April 2020
Bangun Datar | Matematika | Kelas 4 | Tema 4 Berbagai Pekerjaan | Subtema 1 Jenis-jenis pekerjaan...

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