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DeadWolfe
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I know there are some, but I can't think of any examples.
I asked my teacher after class but she couldn't think of any either.
I asked my teacher after class but she couldn't think of any either.
Defining terms is good!Tide said:Define your terms!
Smooth curves are continuous and have a defined slope at every point. They can be drawn without any breaks or sharp angles. On the other hand, analytic curves have a defined derivative at every point and can be expressed as a power series.
A common example is the absolute value function, y = |x|. It is continuous and has a defined slope at every point, but is not analytic because it is not differentiable at x = 0.
Yes, smooth curves are commonly used to model natural phenomena in physics and engineering. For example, the motion of a pendulum can be described by a smooth curve, even though it is not analytic due to the point where the pendulum stops and changes direction.
One way is to check if the curve has a continuous derivative at every point. If there are any breaks or sharp angles in the curve, it is not smooth. Another way is to try to express the curve as a power series. If it cannot be expressed in this form, it is not analytic.
Yes, smooth curves allow for more flexibility and can better approximate real-world phenomena. They are also easier to work with mathematically compared to analytic curves, which require more complex calculations. However, analytic curves have the advantage of being able to provide exact solutions to certain problems.