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Question : 68 of 160
Marks:
+1,
-0
Solution:
Let
f(x)=(sin‌x)sin‌x and
s=log‌f(x)=sin‌x.log‌sin‌x =sin‌x.+(log‌sin‌x)‌cos‌x =cos‌x(1+log‌sin‌x) =cos‌x(.cos‌x) −sin‌x(1+log‌sin‌x) =−sin‌x(1+log‌sin‌x) Now
=0⇒cos‌x=0 or
1+log‌sin‌x=0 ⇒x= or
sin‌x=e−1 ()x==0−1<0⇒f(x) has maximum value
( )sin‌x=e−1= −(1+log‌e−1) =e(1−)>0 ∴ f(x) has minimum when
sin‌x= Minimum value
=[f(x)]sin‌x==() =e−
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