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If y=f(X) and ycos X +Xcos y=π for x€ (-r,r),where r>0,then the greatest integer less than the value of f"(0) is?

If y=f(X) and ycos X +Xcos y=π for x€ (-r,r),where r>0,then the greatest integer less than the value of f"(0) is?

Grade:11

1 Answers

Aditya Gupta
2075 Points
2 years ago
differentiating wrt x, we get
y’cosx – ysinx+cosy – xy’siny=0
differentiating wrt x again,
y”cosx – y’sinx – y’siny=y’sinx+ycosx+y’siny+xy”siny+x(y’)^2*cosy
to compute f”(0), put x=0
y” – y’siny=y+y’siny
or y”=y+2y’siny
at x=0, y=π 
so, y”=π
so, f”(0)=π

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