Find a change of parameter t = g(τ ) for the parabolic arc r(t) = t^2i + tj, −1 ≤ t ≤ 1 such that the arc is traced from the point (1, 1) to (1, −1) as τ varies over the interval [0, 4].

Q: Find the arclength of y = 4x³/2 on 1 < x < 3

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Q: Consider the curve f(y) = -y + for 1 <y<2. Find the arc length of the curve.

A: The curve is fy=18y4+14y2 where 1≤y≤2. The arc length of the curve fy on the interval a,b is defined…

Q: Parameterize the curve r(t) = (2+ cos 3t, 3 – sin 3t, 4t) using arc length, s, as a parameter. Use t…

A: Given the curve rt=2+cos3t, 3-sin3t, 4t---1. Differentiating, we get vt=r't=-3sin3t,…

Q: Find the arc length of the graph of (v-1)³ = x² 1 <y<5.

A: Given that y−13=x2 and 1≤y≤5. We have to find the arc length of the graph of y−13=x2 and 1≤y≤5.…

Q: For the curve r-y +2xy-y+1=0: a) Find the derivative dy/dx. b) Where do the horizontal tangent lines…

A: follow the next step

Q: Suppose θ(t) measures the minimum angle between a clock’s minute and hour hands in radians. Find,…

A: Given that:  θ (t) measures the minimum angle between a clock’s minute and hour hands in radians. An…

Q: Find the arclength of the curve x = Y = 12/2² t² with 4 ≤ t ≤ 8.

A: We have to find the arc length of the given curve.

Q: x = arccos (1- y)+ /2y-y² for <ys1 sysi

A: