Question

Lim x>0 (sin x)/(tg4x) лимиты¡!!!!!!!!!!!!!

Answer 1

Lim x>0 (sin x)*(cos4x)*4x/(sin4x)*(4x)=1/4

применили первый замечательный предел

Lim x>0 (sin x)/(x)=1

Answer 2

To find the limit of (sin x)/(tan(4x)) as x approaches 0 from the right, we can use the properties of trigonometric limits.

First, we simplify the expression: (sin x)/(tan(4x)) = (sin x)/(sin(4x)/cos(4x))

Next, we can multiply the numerator and denominator by cos(4x) to eliminate the denominator: (sin x)/(tan(4x)) = (sin x * cos(4x))/(sin(4x))

Now, we can apply the limit as x approaches 0: lim(x→0+) (sin x * cos(4x))/(sin(4x))

Using the property lim(x→0) sin x / x = 1, we can rewrite the expression further: = lim(x→0+) [(sin x / x) * (cos(4x) / sin(4x))]

Since lim(x→0) sin x / x = 1, the limit of the numerator becomes cos(0) = 1: = lim(x→0+) [(1) * (cos(4x) / sin(4x))]

Now, we need to find the limit of cos(4x) / sin(4x) as x approaches 0.

By applying the limit properties again, we can rewrite the expression: lim(x→0) (cos(4x) / sin(4x)) = lim(x→0) (1 / tan(4x))

Using the property lim(x→0) tan x / x = 1, we can simplify further: = lim(x→0) (1 / (4x / x)) = lim(x→0) (1 / 4) = 1/4

Therefore, the limit of (sin x)/(tan(4x)) as x approaches 0 from the right is 1/4.