How to Simplify Math Expressions with Powers When Finding Limits

lim x->∞ pow top = pow bottom

To simplify expression, we need to know the specific functions or variables represented by “pow top” and “pow bottom

To simplify expression, we need to know the specific functions or variables represented by “pow top” and “pow bottom.” Without that information, it is difficult to provide a detailed answer. However, I can give you a general understanding of how to approach limits involving powers.

In many cases, when we take the limit of a function as x approaches infinity (x → ∞), the dominant term or the term with the highest power in the numerator and denominator determines the limit.

Consider the following generic expression:
lim x → ∞ (a_n * x^n + a_(n-1) * x^(n-1) + … + a_1 * x + a_0) / (b_m * x^m + b_(m-1) * x^(m-1) + … + b_1 * x + b_0)

Here, the exponents n and m represent the highest powers of x in the numerator and denominator, respectively. The coefficients a_n, a_(n-1), …, a_0, b_m, b_(m-1), …, b_0 are constants.

If n > m, then the limit of the expression as x approaches infinity is either positive infinity (∞) or negative infinity (-∞), depending on the sign of the leading terms involving x^n.

If n < m, then the limit is zero (0) since the denominator grows faster than the numerator. If n = m, you need to investigate the coefficients of the leading terms to determine the limit. If the ratio of the coefficients a_n / b_m is not zero, then the limit as x approaches infinity is either positive infinity (∞) or negative infinity (-∞), depending on the signs of a_n and b_m. If the ratio a_n / b_m is zero, the limit is zero (0). So, to find the limit in your specific expression "lim x->∞ pow top = pow bottom,” you need to provide more details about the functions or variables involved in “pow top” and “pow bottom.”

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