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

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

Expert Solution

milcah answered 2 years ago

1). Find the dervatives dy/dx and d^2/dx^2 , and evaluate them at t = 2. x...

1). Find the dervatives dy/dx and d^2/dx^2 , and evaluate them at t = 2. x = t^2 , y= t ln t 2) Find the arc length of the curve on the given interval. x = ln t , y = t + 1 , 1 < or equal to t < or equal to 2 3) Find the area of region bounded by the polar curve on the given interval. r = tan theta , pi/6 < or...

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