Question

Определите четность или нечетность функции y=5/x+3x Обязательно решение нужно. Найдите наименьший положительный период функции y=0,5cos(0,25x-П/3). Оюязательно решениепожалуйста умоляю сделайте

Answer 1

X=20cos pi/20 градусов

Answer 2

Determining the Parity of the Function y=5/x+3x

To determine the parity of the function y=5/x+3x, we need to check if the function is even, odd, or neither.

A function is even if f(x) = f(-x) for all x in the domain, and it is odd if f(x) = -f(-x) for all x in the domain. If neither of these conditions holds, the function is neither even nor odd.

Let's start by analyzing the given function.

The function y=5/x+3x can be split into two separate functions: y=5/x and y=3x. We'll analyze each part separately to determine their parity.

1. Analyzing y=5/x: - The function y=5/x can be considered as f(x) = 5x^(-1). - This function is neither even nor odd, as f(x) ≠ f(-x) and f(x) ≠ -f(-x).

2. Analyzing y=3x: - The function y=3x is a linear function. - A linear function is neither even nor odd, as it does not satisfy the conditions for even or odd functions.

Since both parts of the given function are neither even nor odd, the function y=5/x+3x is also neither even nor odd.

Finding the Smallest Positive Period of the Function y=0.5cos(0.25x-π/3)

To find the smallest positive period of the function y=0.5cos(0.25x-π/3), we can use the formula for the period of a cosine function.

The period of a cosine function of the form y=acos(bx+c) is given by the formula: Period = (2π)/|b|

In the given function y=0.5cos(0.25x-π/3), the value of b is 0.25.

Using the formula, we can calculate the period as follows: Period = (2π)/|0.25| = 8π

Therefore, the smallest positive period of the function y=0.5cos(0.25x-π/3) is 8π.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.