True or FalseFor any polynomial p(x), Lim p(x) = ∞x→∞
The statement is false
The statement is false.
The notation “Lim p(x) = ∞ as x approaches ∞” means that the limit of the polynomial p(x) as x approaches infinity is equal to infinity. This implies that as x gets larger and larger, the value of p(x) also gets arbitrarily large.
If the polynomial p(x) has a non-zero constant term (a term that does not involve any x), then its limit as x approaches infinity will not be infinity. For example, consider the polynomial p(x) = 5. As x approaches infinity, p(x) is always 5, so the limit is not equal to infinity.
However, if the polynomial p(x) is a monomial of the form ax^n, where a is a non-zero constant and n is a positive integer, then the limit as x approaches infinity will be infinity. This is because as x gets larger and larger, the term ax^n dominates any other term in the polynomial, and the value of p(x) becomes arbitrarily large.
So, in general, the limit of a polynomial p(x) as x approaches infinity is not always equal to infinity. It depends on the specific form and degree of the polynomial.
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