In: 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 the given interval.
r = tan θ, π/6 ≤ θ ≤ π/3
4. Find the length of the polar curve on the given interval. (12 points)
r = θ, 0 ≤ θ ≤ π/2