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Calculus and vectors (CURVE SKETCHING) Please show all work in mathematical format/steps so I can understand, I asked this question before but tutor did not

Calculus and vectors (CURVE SKETCHING)

Please show all work in mathematical format/steps so I can understand, I asked this question before but tutor did not answer it properly, so please do it properly in steps leading to answer!

1. Sketches for this question.

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