AP Calculus AB : Comparing relative magnitudes of functions and their rates of change

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

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Example Question #121 : Asymptotic And Unbounded Behavior

Evaluate the limit:

 

Possible Answers:

The limit does not exist

Correct answer:

Explanation:

When evaluating the limit as x approaches infinity, we must compare the magnitude of the functions. The exponential function in the numerator grows faster than the polynomial function (and any polynomial, for that matter) in the denominator, so the numerator dominates and the limit equals 

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