Let f(x) = sin^10(x) − cos(x), 0

Question

Let f(x) = sin^10(x) − cos(x), 0 <= x<=pi  . Show that there is a solution of f(x) = 0
in (0,pi ) please help

michele_laino · Answer

the function $f(x)$ is continuous inside all the real line, furthermore, we have:
$f(0)=-1$, and $f(\pi)=1$
so what can you conclude?

anonymous · Answer

I did this, but I didn't how to complete the answer... please, can you just explain to me.. it may come in the final test

michele_laino · Answer

such $continuous$ function takes all values inside the set $[-1,1]$, so there exists, inside the interval $[0, \pi]$, at least one point $x_0$, such that: $f(x_0)=0$

michele_laino · Answer

since such function have to go in a $continuous$ way, from negative values to positive values

anonymous · Answer

So, what is the point,that will lead the equation to be zero??? please help

michele_laino · Answer

the point is that the function is continuous, so, it has to take all values between $-1<0$ and $1>0$, hence , such function will be equal to zero at least one time inside $[0,\pi]$

anonymous · Answer

thank yooooooooooooooooooooooou so much,,, I got it.......

michele_laino · Answer

the continuity is the key property

michele_laino · Answer

:)