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Problems
Mathematics
Mathematics
Problem
Statement I
The equation
x
3
4
−
sin
π
x
+
2
3
=
0
\frac{x^3}{4} - \sin \pi x + \frac{2}{3} = 0
4
x
3
−
sin
π
x
+
3
2
=
0
has atleast one solution in
[
−
2
,
2
]
[-2, 2]
[
−
2
,
2
]
.
Statement II
Let
f
:
[
a
,
b
]
→
R
f: [a, b] \to R
f
:
[
a
,
b
]
→
R
be a function and
c
c
c
be a number such that
f
(
a
)
<
c
<
f
(
b
)
f(a) < c < f(b)
f
(
a
)
<
c
<
f
(
b
)
, then there is atleast one number
n
∈
(
a
,
b
)
n \in (a, b)
n
∈
(
a
,
b
)
such that
f
(
n
)
=
c
f(n) = c
f
(
n
)
=
c
.
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