Urinma va normal

⭐ — imtihonda eng ko'p ishlatiladigan formulalar. · 🟢 — masalani tezlashtiradi · 🟡 — ilg'or daraja · 🔵 — chuqur o'rganish (olimpiada darajasi)

Urinma va normal ($(x_1, y_1)$ nuqtada)

• ⭐ Urinma gradienti: $m_1 = \dfrac{dy}{dx}$ ning $x = x_1$ dagi qiymati
• ⭐ Normal gradienti: $m_2 = -\dfrac{1}{m_1}$
• Urinma tenglamasi: $y - y_1 = m_1(x - x_1)$
• Normal tenglamasi: $y - y_1 = m_2(x - x_1)$

🟢 Ikki egri chiziqning urinishi

$f$ va $g$ $x_0$ nuqtada urinsa: $\;f(x_0) = g(x_0)$ va $f'(x_0) = g'(x_0)$

🟢 Tashqi nuqtadan urinma

$P(p, q)$ egri chiziqda yotmasa: urinish nuqtasini $(t, f(t))$ deb oling. Urinma $y - f(t) = f'(t)(x - t)$ $P$ dan o'tishi kerak — shundan $t$ ni topasiz.