Question: Which function approaches 0 faster as x approaches infinity: 1/1 + x2 or 1/1 + x. Many improper integrals can be evaluated by comparing functions

Which function approaches 0 faster as x approaches infinity: 1/1 + x2 or 1/1 + x.
Many improper integrals can be evaluated by comparing functions with the method of leading behavior. State which of the given pair of functions approaches its limit more quickly, and demonstrate the result with L'Hopital's rule when needed.

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