Berilgan $$ f(x) $$ funksiyaning eng kichik musbat davrini toping: $$ \begin{array}{ll} ext { a) } f(x)=\sin \frac{3 x}{2}+\operatorname{tg} 7 x & ext { b) } f(x)=\cos x+2 \sin \left(\frac{3 x}{5}+\frac{\pi}{6} ight) \ ext { c) } f(x)=\operatorname{ctg}(x-1)-3 \sin 3 x & ext { d) } f(x)=\sin 3 x+\cos \frac{3 x}{4}+\frac{1}{2} \operatorname{tg} \frac{9 x}{5}\end{array} $$

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Berilgan $$ f(x) $$ funksiyaning eng kichik musbat davrini toping: $$ \begin{array}{ll}	ext { a) } f(x)=\sin \frac{3 x}{2}+\operatorname{tg} 7 x & 	ext { b) } f(x)=\cos x+2 \sin \left(\frac{3 x}{5}+\frac{\pi}{6}ight) \ 	ext { c) } f(x)=\operatorname{ctg}(x-1)-3 \sin 3 x & 	ext { d) } f(x)=\sin 3 x+\cos \frac{3 x}{4}+\frac{1}{2} \operatorname{tg} \frac{9 x}{5}\end{array} $$

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Okay, men bu matematik masalani solishimiz kerak. Berilgan funksiyalarning eng kichik musbat davrini topishimiz kerak. Bu davrlar funksiyalarning periodlari bo'lib, periodning nisbatan kichikroq qiymatlarini topishimiz kerak.

Birinchi, ma'lumotlarni o'qiyman. Funksiyalar sin, cos, tan, cot funksiyalari bilan tashkil topilgan. Bu funksiyalarning periodlari juda muhim. Misol uchun, sin x funksiyasi 2π periodga ega, cos x da 2π, tan x esa π periodga ega. Cot x da ham π periodga ega.

Shu sababli, barcha funksiyalarning periodlarini topishimiz kerak. Ushbu periodlarni aniq qilish uchun, har bir funksiya periodini topib, uning nisbatan kichikroq qiymatini topishimiz kerak.

A) f(x) = sin(3x/2) + tan(7x)
- sin(3x/2) periodi 4π/3
- tan(7x) periodi π/7
Eng kichik periodni topish uchun, 4π/3 va π/7 ni aniq qilishimiz kerak. 4π/3 ≈ 4.1888, π/7 ≈ 0.4488. Shuning, tan(7x) funksiyasi eng kichik periodga ega.

B) f(x) = cos x + 2 sin(3x/5 + π/6)
- cos x periodi 2π
- sin(3x/5 + π/6) periodi 10π/3
Eng kichik periodni topish uchun, 2π va 10π/3 ni aniq qilishimiz kerak. 2π ≈ 6.2832, 10π/3 ≈ 10.472. Shuning, cos x funksiyasi eng kichik periodga ega.

C) f(x) = cot(x - 1) - 3 sin 3x
- cot(x - 1) periodi π
- sin 3x periodi 2π/3
Eng kichik periodni topish uchun, π va 2π/3 ni aniq qilishimiz kerak. π ≈ 3.1416, 2π/3 ≈ 2.0944. Shuning, sin 3x funksiyasi eng kichik periodga ega.

D) f(x) = sin 3x + cos(3x/4) + (1/2) tan(9x/5)
- sin 3x periodi 2π/3
- cos(3x/4) periodi 8π/3
- tan(9x/5) periodi 10π/9
Eng kichik periodni topish uchun, 2π/3, 8π/3, va 10π/9 ni aniq qilishimiz kerak. 2π/3 ≈ 2.0944, 8π/3 ≈ 8.3776, 10π/9 ≈ 3.4907. Shuning, sin 3x funksiyasi eng kichik periodga ega.

Shu sababli, har bir funksiya periodini aniq qilishimiz kerak va uning nisbatan kichikroq qiymatini topishimiz kerak. A) da tan(7x) funksiyasi eng kichik periodga ega, shuning uchun bu variant eng kichik musbat davrini olishimiz mumkin.

A) f(x) = sin(3x/2) + tan(7x) - bu funksiya eng kichik musbat davri mavjud.

Berilgan funksiyaning eng kichik musbat davrini toping:

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