Science:Math Exam Resources/Courses/MATH100/December 2015/Question 10 (c)/Solution 1

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As , the rate at which the exponential function decays to zero is much faster than the rate at which the two linear functions and grow; therefore

More rigorously, we can apply l'Hospital's rule twice to compute that

On the other hand, as , we have , , and , so

Therefore the only asymptote of the function is the line .