lim x->∞ pow top < pow bottom
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To determine the limit as x approaches infinity of the fraction pow top divided by pow bottom, we need to analyze the degree of the numerator and denominator.
If the degree of the numerator is less than the degree of the denominator, then the limit will be zero as x approaches infinity. This is because as x becomes very large, the denominator will grow faster than the numerator and the fraction will approach zero.
If the degree of the numerator is equal to the degree of the denominator, then we can apply L’Hopital’s rule, which states that if we differentiate the numerator and denominator with respect to x and the resulting limit is still in an indeterminate form (such as 0/0 or infinity/infinity), we can continue to differentiate until we obtain a limit that is not indeterminate.
If the degree of the numerator is greater than the degree of the denominator, then the limit will be infinity as x approaches infinity. This is because as x becomes very large, the numerator will grow faster than the denominator and the fraction will approach infinity.
Without more specific information about the expressions pow top and pow bottom, it is difficult to determine the precise value of the limit. However, following the above principles should provide a good starting point for determining the limit.
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