This article investigates the behaviour of two equations, sqrt(cos(x))*cos(300x)+sqrt(abs(x))-0.7)*(4-x*x)^0.01 and sqrt(6-x^2) and -sqrt(6-x^2), from -4.5 to 4.5. We will look into the properties of each equation and examine how they behave in this range.

## Investigating the Behaviour of sqrt(cos(x))*cos(300x)+sqrt(abs(x))-0.7)*(4-x*x)^0.01

This equation has several distinct properties. First, the cosine of 300x is an oscillating function which means that it will vary in a periodic manner with peaks and troughs. The absolute value of x will always be positive, but the square root of this will cause a decrease as x moves from positive to negative values. The fourth-degree polynomial (4-x*x)^0.01 will cause a decrease in the equation as x increases, and the overall result is a complex oscillating function with a decreasing trend.

## Examining sqrt(6-x^2) and -sqrt(6-x^2) from -4.5 to 4.5

The second equation is simpler than the first. In this equation, the square root of 6-x^2 will always be positive and will decrease as x increases. The negative version of this equation will be the same shape but with a negative sign, so it will increase as x increases.

In conclusion, we have examined the behaviour of two equations from -4.5 to 4.5. The first equation is a complex oscillating function with a decreasing trend, while the second equation is a simple decreasing or increasing function depending on the sign.

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