If ( 1 + l / 1-l )⁴p = 1 find the least value of p
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Answer:
sinx
4
+
1−sinx
1
=a ....(1)
f(x)=
sinx
4
+
1−sinx
1
f
′
(x)=cosx(
(1−sinx)
2
1
−
sin
2
x
4
)
=cosx
sin
2
x(1−sinx)
2
(2−sinx)(3sinx−2)
For maxima or minima, f
′
(x)=0
⇒sinx=2(not possible) , sinx=
3
2
and cosx=0⇒x=
2
π
⇒x=sin
−1
3
2
f(sin
−1
3
2
)=6+3=9
f(0
+
)→∞
f(
2
π
−
)→∞
⇒a=9 (by (1))
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