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`        If f(x) = xe-( 1/mod x +1/x) for x not equal to 0 and f(0)=0 then prove that f(x) is continuous for all x but not diffrentiable at x = 0 `
one year ago

```							f(x)= xe^(-2x) when x>0And x when xSo obviously it is continuous on the real line except possibly at zero. So we check rhl and lhl separatelyLhl at zero= 0 Rhl at zero= limit x tends to zero plus x/e^2/x= 0/infinite= 0. Since both limit are equal, and also f(0)= 0, the function is continuous at zero as well.Hence it is continuous.For differentiability, f'(0-)= x/x=1f'(0+)= Lt(xe^-2/x)/x= 0 so it is not differentiable at x=0
```
one year ago
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