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Most Important Selected Qs for JEE AdvancedMathematicsLimits

Let f be a real valued derivable function such that f(x) f(y)=f(x) y+x f(y), x, y R . If f^ (0)=2 then find _ x 0 [ f(x) x ] . [Note: [] represents greatest integer function.]

Correct answer

2

Step-by-step solution

aligned & f(x) f(y) x y = f(x) x + f(y) y & Let F(x)= f(x) x & aligned array rlrl & F(0) & = _ x 0 f(x) x = _ x 0 f^ (x) 1 =2 & F(x) F(y) & =F(x)+F(y) Putting y & =0,2 F(x)=F(x)+2 F(x)=2 & & f(x) & =2 x & & _ x 0 [ 2 x x ] & =2 array

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