Home
Random
Log in
Settings
Donate
About Wikiversity
Disclaimers
Search
Continuous function/x sin 1 over x/On 0,1/Infinitely many zeroes/Exercise
Language
Watch
Edit
Prove that the function
f
(
x
)
=
{
x
sin
1
x
for
x
∈
]
0
,
1
]
,
0
for
x
=
0
,
{\displaystyle f(x)={\begin{cases}x\sin {\frac {1}{x}}{\text{ for }}x\in {]0,1]},\\0{\text{ for }}x=0,\end{cases}}}
is continuous and that it has infinitely many zeros.
Create a solution