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תרגיל באינפי דוגמא 28.1.10 - היסטוריית גרסאות
2026-04-17T05:25:26Z
היסטוריית הגרסאות של הדף הזה בוויקי
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ארז שיינר: דף חדש: <math> \lim_{x\rightarrow \frac{\pi}{2}} 2xtg(x)-\frac{\pi}{cos(x)}= \lim_{x\rightarrow \frac{\pi}{2}} \frac{2xsin(x)}{cos(x)}-\frac{\pi}{cos(x)} = \lim_{x\rightarrow \frac{\pi}{2}} \fr…
2010-01-28T14:10:18Z
<p>דף חדש: <math> \lim_{x\rightarrow \frac{\pi}{2}} 2xtg(x)-\frac{\pi}{cos(x)}= \lim_{x\rightarrow \frac{\pi}{2}} \frac{2xsin(x)}{cos(x)}-\frac{\pi}{cos(x)} = \lim_{x\rightarrow \frac{\pi}{2}} \fr…</p>
<p><b>דף חדש</b></p><div><math><br />
\lim_{x\rightarrow \frac{\pi}{2}} 2xtg(x)-\frac{\pi}{cos(x)}=<br />
\lim_{x\rightarrow \frac{\pi}{2}} \frac{2xsin(x)}{cos(x)}-\frac{\pi}{cos(x)} =<br />
\lim_{x\rightarrow \frac{\pi}{2}} \frac{2xsin(x)-\pi}{cos(x)} =<br />
</math><br />
<br />
<br />
<math><br />
=\lim_{\Delta x\rightarrow 0} \frac{2(\frac{\pi}{2} + \Delta x)sin(\frac{\pi}{2} + \Delta x)-\pi}{cos(\frac{\pi}{2} + \Delta x)} =<br />
\lim_{\Delta x\rightarrow 0} \frac{2(\frac{\pi}{2} + \Delta x)cos(\Delta x)-\pi}{-sin(\Delta x)} =<br />
</math><br />
<br />
<br />
<math><br />
=\lim_{\Delta x\rightarrow 0} \frac{\pi cos(\Delta x)-\pi}{sin(\Delta x)} + 2cos(\Delta x)\frac{\Delta x}{-sin(\Delta x)}=<br />
</math><br />
<br />
<br />
<math><br />
\lim_{\Delta x\rightarrow 0} \frac{\pi [cos(\Delta x)-1]}{\Delta x}\frac{\Delta x}{sin(\Delta x)} + 2cos(\Delta x)\frac{\Delta x}{-sin(\Delta x)}=<br />
\pi \cdot 0 \cdot 1 + 2 \cdot 1 \cdot (-1) = -2<br />
<br />
<br />
</math></div>
ארז שיינר