IIT JAM (2022) | Function Of One Variable | Mathematics | Paper Solution

IIT JAM (2022) | Mathematics | Question Paper
IIT JAM (2022) | Mathematics | Answer Key
#IIT_JAM #Function_of_one_variable #Mathematics #Math_World
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[raghavendrakulkarni]

Sir, I don't think we can take d(uu')/dx simply as k. Because, it is positive for all x >=0. So, d(uu')/dx can any be varying function but all the values are positive. It cannot be assumed a constant function.
Instead we can arrive at the result uu'>0 like this :-
Let g(x) = u(x)u'(x)
Since d(uu')/dx > 0, g'(x) > 0
g(x) is an increasing function
So, x > 0 implies g(x) > g(0)
Now, g(x) > u(0)u'(0)
g(x) > 0 as both u(0) and u'(0) are positive.
Thus, g(x) > 0 for all x>=0
Thus, u(x) u'(x) > 0 for all x>=0
Then we can proceed.
I thought in this way. Is this correct ?

[shivprakash]

Sir e*x equal cosx +isinx kaise ho gya Hx mein