First time i did this question in definite integration class test i just assumed that f will be odd without working that part out luckily i was saved. 😅
A fster method would be to notice that g(x).ln part is an even function Integrating an even function(definite integration) give odd function Thus f(x) is odd and integrate f(x) gives 0
A much faster method would be to know somehow f(x) would have to be zero as can't intrgrate without it to get a value😂.. And assuming that integrare the 2nd part and find the answer
@@rankpolin2287 ln(1-t/1+t) is odd and g(x) is odd Multiplying two odd functions, we get an even function Aur mainebhi aise hi under 4 min solve Kiya tha ye assume karke ki f(x) ka integration zero hoga 🤣🙏
Sir please evaluate this question Let f : ( − ∞ , ∞ ) − { 0 } → R f : ( − ∞ , ∞ ) − { 0 } → R be a differentiable function such that f ′ ( 1 ) = lim a → ∞ a ^2 f ( 1 /a ) . Then lim a → ∞ a ( a + 1 )/2 tan^− 1 ( 1/a ) + a^2 − 2 log e a is equal to
First time i did this question in definite integration class test i just assumed that f will be odd without working that part out luckily i was saved. 😅
I did the same. But it was quite obvious if you observe it.
Yes i also did the same
A fster method would be to notice that g(x).ln part is an even function
Integrating an even function(definite integration) give odd function
Thus f(x) is odd and integrate f(x) gives 0
A much faster method would be to know somehow f(x) would have to be zero as can't intrgrate without it to get a value😂.. And assuming that integrare the 2nd part and find the answer
Also g(x) is odd its given... Why will we assume it to be even😅
@@rankpolin2287 ln(1-t/1+t) is odd and g(x) is odd
Multiplying two odd functions, we get an even function
Aur mainebhi aise hi under 4 min solve Kiya tha ye assume karke ki f(x) ka integration zero hoga 🤣🙏
is integrating an even function always supposed to give us an odd funcn?
@@dazzlekazzle if you don't take the integration constant...which ofc will not come if you integrate from a to x such that f(a)=0
Love your consistency.
Way to go❤
Kohli is also very consistent 😂
Sir please evaluate this question
Let f : ( − ∞ , ∞ ) − { 0 } → R f : ( − ∞ , ∞ ) − { 0 } → R be a differentiable function such that f ′ ( 1 ) = lim a → ∞ a ^2 f ( 1 /a ) . Then lim a → ∞ a ( a + 1 )/2 tan^− 1 ( 1/a ) + a^2 − 2 log e a is equal to
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Ez in 2 mins
U mean gave up in 2 mins ezz??😂😂