3. Consider the curve whose parametric equations are given by r = t2, y = t3. (a) Use the formula for parametric curves to find the arc length from t = 0 to t = 2. (b) By eliminating the parameter t, find the cartesian form of this curve and check your result in (a) 2 dy by using the arc length formula L = dx. dx 4. Find the arc length of the curve y = x – 1)3/2 between r = 1 and r = 4. [Use the formula in 3(b).]

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A: The expression for the arc length of the parametric curve is; L=∫abx't2+y't2dt   Given: xt=3+3t2 ;…

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Q: Find the arc length of the parametric curve. = 4 cos(t), y = 4 sin(t), % = 3t; 0 < t < T L =

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Q: (a) Find the tangent line(s) to the parametric curve given by x(t) = t° – 4t", and y(t) = t. at the…

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A: We have given;

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A: We have to set up the integral that gives the arc length of C.

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A: Given parametric equations - x = t2-1t2 = x+1t = x+1         .................(1)y =…

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A: Follow the procedure given below

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Q: Find the arc length of the curve on the given interval. Parametric Equations     x = √t, y = 3t − 1…

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A: take derivative

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A: Take the derivative of x and y with respect to t then use the formula for the arc length.

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A: Consider the parametric equations  x = t2 − 1 and y = t2 + 2t

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