Osculating Circle Homework: Solving for Curvature Limit

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Adeel Ahmad
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Homework Statement


upload_2016-11-8_20-30-48.png


I know I would use the curvature equation |f''| / [1-(f')^2]^3/2 and then take the limit of that to -1. I just don't understand why I have to take the limit of the curvature and when I take the limit of the curvature I get |-1| / (13)^3/2 when the answer should be 2.
 
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This is my work:
 

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