\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Courses
About
Login
Register
C
⌫
\(\pi\)
e
\(\frac{a}{b}\)
!
←
→
(
)
\(\sqrt{\,}\)
\(a^{b}\)
7
8
9
\(\div\)
log
ln
4
5
6
\(\times\)
cos
cos⁻¹
1
2
3
-
sin
sin⁻¹
0
.
=
+
tan
tan⁻¹
Let \(f\) be the function defined on \(\mathbb{R}\) by:$$ f(x) = \dfrac{2\cos(x) + 1}{2 + \cos(x)} $$
Show that the function \(f\) is \(2\pi\)-periodic.
Show that the function \(f\) is even.
Deduce that \(f\) can be studied on the interval \([0, \pi]\).
Determine the table of variations of \(f\) on \([0, \pi]\).
Show that the equation \(f(x) = 0\) has exactly one solution \(\alpha\) on \([0, \pi]\) and give an approximate value of \(\alpha\) to the nearest thousandth.
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.
Exit