Q.Nilai dari \displaystyle \tt \lim_{x \to \frac{\pi}{4}} \frac{sin \: 2x}{sin \: x + cos \: x} =.... Question from @anitasamosir17

misrokhah439

Nilai Dari:

$\displaystyle \tt \lim_{x \to \frac{\pi}{4}} \frac{sin \: 2x}{sin \: x + cos \: x}$

$= \tt \frac{sin \: \frac{\pi}{2} }{sin \: \frac{\pi}{4} + cos \frac{\pi}{4} }$

$= \tt \frac{1}{ \frac{1}{2} \sqrt{2} + \frac{1}{2} \sqrt{2} }$

$= \tt \frac{1}{ \sqrt{2} }$

$= \tt \frac{1}{2} \sqrt{2}$

4 votes Thanks 5

myiinx Tp :-:

myiinx tu..// Tp :v

misrokhah439 tidak semudah itu, ini sy yang req, tapi req asal sy belum tau jawabannya, jadi sy tetap mikir jawabnya ;-;

myiinx :-::

myiinx wiraa blm tau cara pake latex_.

misrokhah439 berarti sy gk salh (⌐■‿■)

Eutopya Ntah apa yang kalian bahas dari tadi ;-;

Eutopya

Jawaban:

½√2

Penjelasan dengan langkah-langkah:

$\displaystyle \tt \lim_{x \to \frac{\pi}{4}} \frac{sin \: 2x}{sin \: x + cos \: x}$

$\displaystyle \tt \lim_{x \to \frac{\pi}{4}} \frac{sin \: (2 \times \frac{\pi}{4}) }{sin \: ( \frac{\pi}{4})+ cos \: (\frac{\pi}{4})}$

$\displaystyle \tt \: \: \: \: \: \: = \frac{1}{\frac{1}{2}\sqrt{2}+\frac{1}{2}\sqrt{2}}$

$\displaystyle \tt \: \: \: \: \: \: = \frac{1}{(\frac{1}{2}+\frac{1}{2})\sqrt{2}}$

$\displaystyle \tt \: \: \: \: \: \: = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} }$

$\displaystyle \tt \: \: \: \: \: \: = \frac{1 \sqrt{2} }{ \sqrt{4} }$

$\displaystyle \tt \: \: \: \: \: \: = \frac{1}{2} \sqrt{2}$

$\\$

>> Trigonometri Sudut Istimewa

$\boxed{\begin{array}{c|c|c|c|c|c|c|c}\sf & \sf 0° & \sf 30° & \sf 37° & \sf 45° & \sf 53° &\sf 60° &\sf 90° \\\hline\sf sin & \sf 0 & \sf \frac{1}{2} & \sf\frac{3}{4} & \sf \frac{1}{2}\sqrt{2} & \sf\frac{4}{5} &\sf\frac{1}{2}\sqrt{3} & \sf 1\\\hline\sf cos & \sf 1 &\sf\frac{1}{2}\sqrt{3} & \sf\frac{4}{5} &\sf \frac{1}{2}\sqrt{2} & \sf\frac{3}{4} &\sf\frac{1}{2} & \sf 0 \\\hline\sf tan &\sf 0 & \sf\frac{1}{3}\sqrt{3} & \sf\frac{3}{4} & \sf 1 & \sf\frac{4}{3} & \sf\sqrt{3} & \sf\infty \end{array}}$

$\boxed{\begin{array}{c|c|c}\sf x & \sf sin~x &\sf cos~x\\\hline\sf 0 & \sf 0 & \sf 1\\\hline\sf\frac{\pi}{6} & \sf\frac{1}{2} & \sf\frac{1}{2}\sqrt{3}\\\hline\sf\frac{\pi}{4} &\sf\frac{1}{2}\sqrt{2} & \sf\frac{1}{2}\sqrt{2} \\\hline\sf\frac{\pi}{3} & \sf\frac{1}{2}\sqrt{3} & \sf\frac{1}{2} \\\hline\sf\frac{\pi}{2} & \sf 1 & \sf 0 \\\hline\sf\pi & \sf 0 & \sf -1 \end{array}}$

5 votes Thanks 14

UserNpcMod123 cilly mau lesby sm basih?

Eutopya Nggaklah ;-;

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