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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 |
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Answer» 0 `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`. |
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