1. Muammo: Toq funksiyalarni aniqlash. Toq funksiya uchun shart: $$f(-x) = -f(x)$$ har qanday $x$ uchun. 2. Berilgan funksiyalar: 1) $$f(x) = x^3 \sin x$$ 2) $$f(x) = x^2 \cos x$$ 3) $$f(x) = x + x^3$$ 3. Har bir funksiyaning toqligini tekshiramiz: - 1-funksiyani tekshirish: $$f(-x) = (-x)^3 \sin(-x) = -x^3 (-\sin x) = -x^3 (-\sin x) = -x^3 (-\sin x) = -f(x)$$ Chunki $$\sin(-x) = -\sin x$$ va $$(-x)^3 = -x^3$$, shuning uchun 1-funksiya toq. - 2-funksiyani tekshirish: $$f(-x) = (-x)^2 \cos(-x) = x^2 \cos x = f(x)$$ Bu funksiya juft, chunki $$f(-x) = f(x)$$. - 3-funksiyani tekshirish: $$f(-x) = -x + (-x)^3 = -x - x^3 = -(x + x^3) = -f(x)$$ Demak, 3-funksiya ham toq. 4. Natija: Toq funksiyalar 1) va 3) funksiyalar. Javob: 1 va 3.