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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
{
x
2
,
−
1
≤
x
≤
1
,
c
x
,
1
<
x
≤
3.
f(x)=\begin{cases}x^{2},&-1\le x\le 1,\\c x,&1< x\le 3.\end{cases}
f
(
x
)
=
{
x
2
,
c
x
,
−
1
≤
x
≤
1
,
1
<
x
≤
3.
If
lim
n
→
∞
∑
i
=
1
n
f
(
−
1
+
4
i
n
)
⋅
4
n
=
14
,
\lim_{n\to\infty}\sum_{i=1}^{n}f\!\left(-1+\tfrac{4i}{n}\right)\cdot\tfrac{4}{n}=14,
n
→
∞
lim
i
=
1
∑
n
f
(
−
1
+
n
4
i
)
⋅
n
4
=
14
,
find the value of the constant
c
c
c
.
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