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Please show work. 1. Find the derivatives dy/dx and d2y/dx and evaluate them at t = 2. x...

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Basic Math

Please show work.

1. Find the derivatives dy/dx and d2y/dx and evaluate them at t= 2.

x = t2, y = tln t

2. Find the arc length of the curve on the given interval

x = ln t, y = t + 1, 1 ≤ t ≤ 2

3. Find the area of region bounded by the polar curve on thegiven interval.

r = tan θ, π/6 ≤ θ ≤ π/3

4. Find the length of the polar curve on the given interval. (12points)

r = θ, 0 ≤ θ ≤ π/2

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