The limit is .

As  becomes large, both numerator and denominator becomes larger.

Hence it is difficult to find the ratio as  becomes large.

To evaluate the limit at infinity of any rational function, divide both the numerator and denominator by the highest power of that occurs in the denominator.

Consider the function .

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Apply the limit

Quotient law of limit : , if .

Sum and difference law of limit : .

Theorem : If is a rational number then .

Therefore .

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