What criteria separates a planet from a dwarf planet?

Answer 1

objects obeying the definition of IAU 2006 is planets.

Other bodies can not be called plantes. Image result for IAU definition of planets A: A planet is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.
defnition IAU from wikipedia.

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Answer 2

Elena Antonova

The criteria that separates a planet from a dwarf planet is that a planet must meet three conditions: it must orbit the Sun, it must be spherical in shape due to its own gravity, and it must have cleared its orbit of other debris. In contrast, a dwarf planet also orbits the Sun and is spherical in shape, but it has not cleared its orbit of other debris, which distinguishes it from a planet.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.