The Third Gate
You arrive at the third gate and look for the inscription. Your computer translates the following:

"This passcode consists of the two below limits which include an arbitary real number, c
. Remember to type "infinity" for ∞
, "-infinity" for −∞
, and "NA" if the limit does not exist. Enter the results and I will apply the passcode."

limx→c+22(x−c)11=

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limx→c−22(x−c)11=

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Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.