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The issue here is that you are assuming that over a small time interval you are considering, you are assuming that the acceleration on the ball is constant. However, the acceleration changes no matter how small of a 'time interval' you consider. $v(t_0+\delta t)=v(t_0)+\frac{dv}{dt}(t_0)\delta t$ is essentially what you are doing: expanding to first order in the derivative of the velocity to figure out what the velocity is at $t_0+\delta t$, which is fine, but there will be an error if you take finite (non-zero) interval of time. This is an identical issue of following a tangent line at, say point (1,0) to the unit circle centre origin. You can approximate a point on the unit circle that is just above this point by following the tangent line, but you will be off by a certain amount. The position vector to that point in the tangent line will have a length slightly greater than one. That error is because by using the tangent line you ignore that the true path, the circle, is continuously curving.