Limit Trigonometri
Penjelasan dengan langkah-langkah:
[tex]\sf 1. lim_{x\to \frac{\pi}{3}}\ \dfrac{tan^2 x + 1}{cos \ x}[/tex]
[tex]\sf subs \ x= \frac{\pi}{3}[/tex]
[tex]\sf =lim_{x\to \frac{\pi}{3}}\ \dfrac{(\sqrt3)^2 + 1}{(\frac{1}{2})}[/tex]
[tex]=\frac{3+1}{\frac{1}{2}} =8\\[/tex]
[tex]\sf 2). lim_{x\to \frac{\pi}{4}} \ \dfrac{sec^2\ x + 4}{sin^2\ x}[/tex]
[tex]\sf subs \ x = \frac{\pi}{4}[/tex]
[tex]\sf lim_{x\to \frac{\pi}{4}} \ \dfrac{sec^2\ \frac{\pi}{4} + 4}{sin^2\ (\frac{\pi}{4})}[/tex]
[tex]\sf lim_{x\to \frac{\pi}{4}} \ \dfrac{(\sqrt 2)^2+ 4}{(\frac{1}{2}\sqrt2)^2}[/tex]
[tex]\sf lim_{x\to \frac{\pi}{4}} \ \dfrac{2+4}{\frac{1}{2}} = 12\\[/tex]
[tex]\sf 3). lim_{x\to 0}\ \dfrac{sin \ 5x+ sin\ 4x}{2x}[/tex]
[tex]\sf lim_{x\to 0}\ \dfrac{ 5x+ 4x}{2x} = \dfrac{9}{2}\\[/tex]
[tex]\sf 4). lim_{x\to 0}\ \dfrac{cot \ 6x}{cot \ 2x}[/tex]
[tex]\sf lim_{x\to 0}\ \dfrac{tan \ 2x}{tan \ 6x} =\dfrac{2}{6} =\dfrac{1}{3}\\[/tex]
[tex]\sf 5). lim_{x\to 0}\ \dfrac{2\sin^2 x }{x.\tan 3x}[/tex]
[tex]\sf lim_{x\to 0}\ \dfrac{2. \sin \ x . \sin x }{x.\tan 3x}[/tex]
[tex]\sf lim_{x\to 0}\ \dfrac{2.(x)(x)}{x(3x)} = \dfrac{2}{3}[/tex]
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