pakee cara
Limit TriGOnometri
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Penjelasan dengan langkah-langkah:
[tex]\sf \lim_{x\to 0}\ \dfrac{\sin 2x (1- \cos x)}{3x. \tan 2x. \sin 5x}[/tex]
[tex]\sf \lim_{x\to 0}\ \dfrac{\sin 2x \{1- (1 - 2 sin^2\ \frac{1}{2}x)\}}{3x. \tan 2x. \sin 5x}[/tex]
[tex]\sf \lim_{x\to 0}\ \dfrac{\sin 2x (2 sin^2\ \frac{1}{2}x)}{3x. \tan 2x. \sin 5x}[/tex]
[tex]\sf \lim_{x\to 0}\ \dfrac{2\sin 2x . \sin\ \frac{1}{2}x. \sin\ \frac{1}{2}x}{3x. \tan 2x. \sin 5x}[/tex]
[tex]\sf \lim_{x\to 0}\ \dfrac{2(2x)(\frac{1}{2}x)(\frac{1}{2}x)}{3x (2x). (5x)}[/tex]
[tex]\sf \lim_{x\to 0}\ \dfrac{2(2)(\frac{1}{2})(\frac{1}{2})}{3 (2). (5)}=\dfrac {1}{30}[/tex]
[tex] \displaystyle \rm \lim_{ x \to0} \: \frac{ \sin(2x) \cdot(1 - \cos(x) )}{3x \cdot \tan(2x ) \sin(5x) } [/tex]
[tex] \displaystyle \rm = \lim_{ x \to0} \: \frac{ \sin(2x)}{3x} \times \lim_{ x \to0} \: \frac{ 1 - \cos(x) }{ \tan(2x ) \sin(5x) } [/tex]
[tex] \displaystyle \rm = \frac{2}{3} \times \lim_{ x \to0} \: \frac{2 \sin ^{2} ( \frac{1}{2}x ) }{ \tan(2x ) \sin(5x) } [/tex]
[tex] \displaystyle \rm = \frac{2}{3} \times \lim_{ x \to0} \: \frac{2 \sin ( \frac{1}{2}x ) \sin( \frac{1}{2}x ) }{ \tan(2x ) \sin(5x) } [/tex]
[tex] \displaystyle \rm = \frac{4}{3} \times \lim_{ x \to0} \: \frac{ \sin( \frac{1}{2}x ) }{ \tan(2x ) } \times \lim_{ x \to0}\frac{ \sin ( \frac{1}{2}x ) }{ \sin(5x) } [/tex]
[tex] \displaystyle \rm = \frac{4}{3} \times \frac{ \frac{1}{2} }{ 2} \times \frac{ \frac{1}{2} }{ 5} [/tex]
[tex] \displaystyle \rm = \frac{4}{3} \times \frac{ 1 }{ 4} \times \frac{1 }{ 10} [/tex]
[tex] \displaystyle \rm = \frac{ \cancel4}{3} \times \frac{ 1 }{ \cancel4} \times \frac{1 }{ 10} [/tex]
[tex] \displaystyle \rm = \frac{1}{30} [/tex]
[answer.2.content]
