The problem involves calculating the limit as x approaches 3 from the right for the expression (81 - x^4) / (x^2 - 6x + 9)^2. The subject area pertains to limits in calculus.
Some participants suggest that substituting 3 leads to an undefined expression, indicating that the limit may not exist. Others propose that the expression diverges as x approaches 3 from the right, with speculation about the nature of this divergence.
There is an ongoing discussion about the behavior of the limit as x approaches 3, particularly regarding the implications of the denominator becoming zero and the resulting divergence.
TheRedDevil18 said:By substituting 3 in the denominator, it would be undefined, so their is no limit ?
Vahsek said:Indeed, substituting 3 means that you would have 0 in the denominator, so the original expression would diverge as x → 3+. Therefore, you could argue that there is no limit since the expression would not converge to any real number per say.
That being said, I feel that a more precise answer is needed. For instance, you could say how it diverges.
TheRedDevil18 said:I'm guessing it would go to negative infinity then ?