Saved Bookmarks
| 1. |
Let `y=f(x)` be satisfying differential equation `e^(-x^(2))(dy)/(dx)=2xy^(2)` such that `f(0)=(1)/(2)` Q. Which of the following statement is correct about `f(x)`?A. `f(x)` is unboundedB. `f(x)` is bijectiveC. `f(x)` is oddD. None of these. |
|
Answer» Correct Answer - A `int(dy)/(y^(2))=int2xe^(x^(2))dx` `-(1)/(y)=e^(x^(2))+C` point `(0.(1)/(2))` lies on the curve `implies-2=1+C` `impliesC=-3` Hence `-(1)/(y)=e^(x^(2))-3` `impliesf(x)=(1)/(3-e^(x^(2)))` Hence, `f(x)` is even which means that it cannot be objective Also, denominator of `f(x)` becomes zero which implies that it cannot be bounded. |
|