Why is that quotient of homogeneous polynomials (each of same degree) in multivariable case bounded?

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I am sorry if this isn’t obvious to me. I was doing questions on limits of multivariable functions and encountered such functions.

Is this because both numerator and denominator decay at same rate as they approach the origin, so they are bounded?

And what can you say about the limit as it tends to origin in this case?

Thanks for your time.