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If
f
(
x
)
=
{
8
x
−
4
x
−
2
x
+
1
x
2
,
x
>
0
e
x
sin
x
+
π
x
+
λ
ln
4
,
x
≤
0
f(x)=\begin{cases}\frac{8^x-4^x-2^x+1}{x^2}, & x>0\\ e^x\sin x+\pi x+\lambda\ln 4, & x\leq 0\end{cases}
f
(
x
)
=
{
x
2
8
x
−
4
x
−
2
x
+
1
,
e
x
sin
x
+
π
x
+
λ
ln
4
,
x
>
0
x
≤
0
…
Mathematics
Problem
If
f
(
x
)
=
{
8
x
−
4
x
−
2
x
+
1
x
2
,
x
>
0
e
x
sin
x
+
π
x
+
λ
ln
4
,
x
≤
0
f(x)=\begin{cases}\frac{8^x-4^x-2^x+1}{x^2}, & x>0\\ e^x\sin x+\pi x+\lambda\ln 4, & x\leq 0\end{cases}
f
(
x
)
=
{
x
2
8
x
−
4
x
−
2
x
+
1
,
e
x
sin
x
+
π
x
+
λ
ln
4
,
x
>
0
x
≤
0
is continuous at
x
=
0
x=0
x
=
0
, then the value of
λ
\lambda
λ
is (a)
4
log
e
2
4\log_e 2
4
lo
g
e
2
(b)
2
log
e
2
2\log_e 2
2
lo
g
e
2
(c)
log
e
2
\log_e 2
lo
g
e
2
(d) none of these
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