PAS MATEMATIKA BLOG: Contoh Soal Lanjutan 2 Limit Fungsi Trigonometri (Matematika Peminatan Kelas XII)

$\begin{array}{ll}\\ 11.&\textrm{Nilai dari}\: \: \underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{15x\tan x}{3x\sin 5x}=....\\ &\begin{array}{ll}\\ \textrm{a}.&\displaystyle \frac{1}{8}\\\\ \textrm{b}.&\displaystyle \frac{1}{6}\\\\ \textrm{c}.&\displaystyle \frac{1}{3}\\\\ \textrm{d}.&\displaystyle \frac{3}{2}\\\\ \textrm{e}.&\displaystyle 1 \end{array} \end{array}$

Jawab : e

$\color{blue}\begin{aligned}\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{ 15x\tan x}{3x\sin 5x}&=\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{\color{red}\textcircled{15}x\tan \textcircled{1}x}{\color{red}\textcircled{3}x\tan \color{red}\textcircled{5}x}\\ &=\displaystyle \frac{15\times 1}{3\times 5}\\ &=\displaystyle \frac{15}{15}\\ &=1 \end{aligned}$

$\begin{array}{ll}\\ 12.&\textrm{Nilai dari}\: \: \underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{18x\tan x}{3x\sin 4x}=....\\ &\begin{array}{ll}\\ \textrm{a}.&\displaystyle \frac{1}{8}\\\\ \textrm{b}.&\displaystyle \frac{1}{6}\\\\ \textrm{c}.&\displaystyle \frac{1}{2}\\\\ \textrm{d}.&\displaystyle \frac{3}{2}\\\\ \textrm{e}.&\displaystyle 2 \end{array} \end{array}$

Jawab : d

$\color{blue}\begin{aligned}\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{ 18x\tan x}{3x\sin 4x}&=\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{\color{red}\textcircled{18}x\tan \textcircled{1}x}{\color{red}\textcircled{3}x\tan \color{red}\textcircled{4}x}\\ &=\displaystyle \frac{18\times 1}{3\times 4}\\ &=\displaystyle \frac{18}{12}\\ &=\displaystyle \frac{3}{2} \end{aligned}$

$\begin{array}{ll}\\ 13.&\textrm{Nilai dari}\: \: \underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{12x\sin x}{2x^{2}}=....\\ &\begin{array}{ll}\\ \textrm{a}.&-\displaystyle \frac{1}{2}\\\\ \textrm{b}.&\displaystyle \frac{1}{2}\\\\ \textrm{c}.&\displaystyle 3\\\\ \textrm{d}.&\displaystyle 6\\\\ \textrm{e}.&\displaystyle 12 \end{array} \end{array}$

Jawab : d

Sebagai pembahasannya adalah sebagai berikut

$\color{blue}\begin{aligned}\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{ 12x\sin x}{2x^{2}}&=\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{\color{red}\textcircled{12}x\sin \textcircled{1}x}{\color{red}\textcircled{2}x\times \textcircled{1}x}\\ &=\displaystyle \frac{12\times 1}{2\times 1}\\ &=\displaystyle \frac{12}{2}\\ &=6 \end{aligned}$

$\begin{array}{ll}\\ 14.&\textrm{Nilai dari}\: \: \underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{\sin^{2} 3x}{12x^{2}}=....\\ &\begin{array}{ll}\\ \textrm{a}.&\displaystyle \frac{1}{4}\\\\ \textrm{b}.&\displaystyle \frac{1}{2}\\\\ \textrm{c}.&\displaystyle \frac{3}{4}\\\\ \textrm{d}.&\displaystyle 4\\\\ \textrm{e}.&\displaystyle 16 \end{array} \end{array}$

Jawab : c

$\color{blue}\begin{aligned}\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{ \sin^{2} 3x}{12x^{2}}&=\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{\color{red}\sin \textcircled{3}x\times \sin \textcircled{3}x}{\color{red}\textcircled{12}x\times \textcircled{1}x}\\ &=\displaystyle \frac{3\times 3}{12\times 1}\\ &=\displaystyle \frac{9}{12}\\ &=\displaystyle \frac{3}{4} \end{aligned}$

$\begin{array}{ll}\\ 15.&\textrm{Nilai dari}\: \: \underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{\tan^{2} 3x}{21x^{2}}=....\\ &\begin{array}{ll}\\ \textrm{a}.&\displaystyle \frac{1}{4}\\\\ \textrm{b}.&\displaystyle \frac{3}{7}\\\\ \textrm{c}.&\displaystyle \frac{3}{4}\\\\ \textrm{d}.&\displaystyle 3\\\\ \textrm{e}.&\displaystyle 7 \end{array} \end{array}$

Jawab : b

$\color{blue}\begin{aligned}\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{ \tan^{2} 3x}{21x^{2}}&=\underset{x\rightarrow \displaystyle 0}{\textrm{Lim}}\: \: \displaystyle \frac{\color{red}\tan \textcircled{3}x\times \tan \textcircled{3}x}{\color{red}\textcircled{21}x\times \textcircled{1}x}\\ &=\displaystyle \frac{3\times 3}{21\times 1}\\ &=\displaystyle \frac{9}{21}\\ &=\displaystyle \frac{3}{7} \end{aligned}$

Sampai di sini semoga ini semua dapat menambah khazanah dalam menyelesaikan permasalahan jika suatu ketika pembaca mendapati soal yang semisal

Semoga bermanfaat

PAS MATEMATIKA BLOG

Contoh Soal Lanjutan 2 Limit Fungsi Trigonometri (Matematika Peminatan Kelas XII)

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