But how do I able to obtain the number r?jbunniii said:In order to get exact equality you need
$$\sin(x) = x - x^3/6 + E(x)$$
where ##E(x)## is the error due to using only two terms. As an approximation, we assume this error to be zero, so we pretend that
$$\sin(x) = x - x^3/6$$
and solve the equation
$$x^2 = x - x^3/6$$
As the problem statement says, ##r## is a nonzero root of the equation ##x^2 = \sin(x)##. You will find an approximation to this by solving the equation ##x^2 = x - x^3/6##.zjhok2004 said:But how do I able to obtain the number r?
Solved, thanks!jbunniii said:As the problem statement says, ##r## is a nonzero root of the equation ##x^2 = \sin(x)##. You will find an approximation to this by solving the equation ##x^2 = x - x^3/6##.
A Taylor Polynomial approximation is a mathematical method used to approximate a function using a polynomial. It is a way to represent a complex function as a simpler polynomial function, making it easier to work with and calculate values.
A Taylor Polynomial approximation is calculated using a formula that involves taking derivatives of the function at a specific point, and then plugging in those derivatives and the point into the formula. The more derivatives that are used, the more accurate the approximation will be.
A Taylor Polynomial approximation is useful because it allows us to approximate a function with a simpler polynomial function, making it easier to work with and calculate values. It also allows us to estimate the behavior of a function near a specific point.
A Taylor Polynomial approximation is a finite polynomial approximation of a function, while a Taylor series is an infinite polynomial representation of a function. The Taylor Polynomial approximation only uses a certain number of derivatives at a specific point, while a Taylor series uses all derivatives of a function at a specific point.
Taylor Polynomial approximation is commonly used in fields such as physics, engineering, and economics, where complex functions need to be simplified and approximated for calculation and analysis. It is also used in computer graphics and numerical analysis.