How to Evaluate the Limit of (Top Exponent) / (Bottom Exponent) as x Approaches Infinity

lim x->∞ pow top < pow bottom

To evaluate the limit as x approaches infinity of (top exponent)/(bottom exponent), we can use the concept of limits of powers

To evaluate the limit as x approaches infinity of (top exponent)/(bottom exponent), we can use the concept of limits of powers.

If both the numerator and denominator have the same power of x, we can divide both the numerator and denominator by the highest power of x to simplify the expression. Let’s represent the highest power of x as n:

lim x->∞ pow(top, n) / pow(bottom, n)

Now, we can rewrite the expression as:

lim x->∞ (pow(top, n) / pow(x, n)) / (pow(bottom, n) / pow(x, n))

Since we are taking the limit as x approaches infinity, the denominator will dominate the expression if its power is higher than that of the numerator. Hence, if the top exponent is less than the bottom exponent (top < bottom), the limit will be 0. Therefore, the limit as x approaches infinity of pow(top, n) / pow(bottom, n), where top < bottom, is 0.

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