2. (i) Describe with a sketch the trace of the following curve in R² (t) = (t² sin(t), t2 cos(t)), (€ -2,2]). [15 Marks] (ii) Find the length of this curve. [25 Marks]

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A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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A: Step 1: Step 2: Step 3: Step 4:

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A: Step 1: Step 2: Step 3: Step 4:

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Q: Show all steps. Correct potential function is: f(x,y) = 3xyz +4y +z^2. Correct evaluation gives -39

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A: Step 1: Step 2: Step 3: Step 4:

Q: Test the series for convergence or divergence.

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A: x=4i+2j​−ky​=−3i+5j​+4kz=−i−j​+2k  ∣∣∣​2x+2y​−z∣∣∣​=∣∣∣​3i+15j​+4k∣∣∣​=32+152+42​=250​≈15.811

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Q: Hi i need help with the problem that is in the attached image.  Thank you so much

A: Step 1:Step 2: Step 3: Step 4: