1.

Let y = f(x) satisfies the differential equation (sin x)dy + (cos x)ydx = e^(x) dx with f(0) = 0. Then the value of lim_(x to 0)f(x) is

Answer»

0
1
`-1`
Does not exist

Solution :`(SIN x) dy + (cos x) ydx = E^(x) dx`
`d[(sin x).y] = e^(x)dx`
Intergrating `ysin x = e^(x) + C`
Putting `f(0) = 0`
`0 = 1 + c implies c = -1`
`y = (e^(x) - 1)/(sin x)`
`lim_(x to 0) (e^(x) - 1)/(x) (x)/(sin x) = 1`.


Discussion

No Comment Found

Related InterviewSolutions