Question

F(X)=2x sinx

Answer 1

f(x)=(sinx)/2x xO=O

Answer 2

f`(x)=2sinx+2xcosx

Answer 3

The given function is $f(x) = 2x \sin(x)$. This function represents a mathematical relationship between the input variable $x$ and the output variable $f(x)$.

In this case, the function multiplies the input variable $x$ by the sine of $x$ and then multiplies the result by 2. The sine function ($\sin(x)$) represents a periodic oscillation between -1 and 1 as the input angle $x$ changes.

By multiplying $2x$ with $\sin(x)$, the function $f(x)$ amplifies the oscillation and scales it by a factor of $2x$. The resulting function value $f(x)$ will depend on the specific value of $x$ that is used as input.

For example, if we evaluate $f(x)$ at $x = \pi$, the function becomes $f(\pi) = 2\pi \sin(\pi)$. Since $\sin(\pi) = 0$, the function value at $x = \pi$ will be $f(\pi) = 0$.

Similarly, for other values of $x$, the function will yield different results. The graph of $f(x)$ will exhibit oscillatory behavior, with the amplitude and frequency determined by the value of $x$.

Note: It's important to clarify whether the input variable $x$ is measured in radians or degrees, as the sine function behaves differently depending on the unit of measurement. The standard convention is to use radians unless stated otherwise.