What on Earth is going on?

Calculus Level 2

Given a polynomial f:R+R+f: \mathbb{R}^+ \rightarrow \mathbb{R}^+ that satisfies f(0)=1,f(1)=e,f(e)=πf(0) = 1, f(1) = e, f(e) =\pi .

Let I=1ef(x)f(x)dx\displaystyle I = \int_1^e \frac{ f'(x) } { f(x) } \, dx . Find the value of sgn(I)\text{sgn}(I) .

Notation: sgn(x)\text{sgn}(x) denote the signum function, where sgn(x)={xx,x00,x=0 \text{sgn}(x) = \begin{cases} \dfrac{x}{|x|} , x \ne 0 \\ 0 , x = 0 \end{cases} .

×

Problem Loading...

Note Loading...

Set Loading...