52. When x < 0, dx/dt > 0 --> x will increase over time and when x reaches 0, then dx/dt becomes 0, so the value of x stays at 0 after that. So, the answer is (b) Increases and approach 0 overtime.
53. When 0<x<1, dx/dt < 0 --> x will decrease over time and when x reach 0, then dx/dt = 0, so the value of x stays at 0 after that. So, the answer is Decreases and approach 0 overtime, therefore, none of the options is correct.
54. When x > 1, dx/dt > 0 --> x will increase over time without any bound. So, the answer is (d).