The student who overcomes this problem might learn the following useful techniques:

• If some expression looks complicated, try graphing it and see if you get any insight into how it behaves.

• Some complicated functions can be understood by breaking them into simple parts and dealing with the parts separately.

• Piecewise-continuous functions can be integrated by breaking them into continuous intervals and integrating the intervals separately.

• You can exploit symmetry to reduce the amount of calculation required.

None of this is deep stuff, but it's all valuable technique. Also they might make the valuable observation that not every problem should be solved by pushing around the symbols.

*I liked this simple calculus exercise* *from* plover.com

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