Reparametrize the curve 2t C : r(t) = i+ -j, t > 0 t2 + 1 with respect to arc length. Simplify your result so that it becomes clear that the curve is a circle (hint: for a unit circle centred at the origin, the polar angle is equal to the arc length from (1, 0)).

Q: (10) Let r(t) = (e'cos 2t, et sin 2t, e2t) %3D a) The curve lies on a quadric surface. Give the…

A: Let y(t) = ( et cos 2t , et sin 2t , e2t ) . Then, we have to identify the quadric surface and it's…

Q: Find the length of the following parametric curve. x = 6 + 916, y = 5 + 6t°, 0<t < 2.

A: solution is given below

Q: Consider the curve parameterized by 1 -t° + 3t2 + 3 2 X = 3 y = r - r? for 0

A: We need to find tangent.

Q: Consider the curve C with parametric equations Sr(t) = t3 – 3t +1 ly(t) = t(t + 1) %3D defined for t…

A: For horizontal tangent slope of tangent is 0 and for vertical tangent slope 10 concavity of y=f(x)…

Q: Find f (x-y3)d a + xy dy if the contour C looks as follows: It consists of two arcs of radius 1 and…

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Q: 5 x = = 5 In((t/6)? – 1) from t = 7 to t = 9.

A:

Q: 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t = 2n. %3D 2. Find the length…

A: As we know that, The expression for the length of vector-valued curve is: L=∫abx't2+y't2dt   1).…

Q: Calculare 13ydz t 13x'y dy, Where Cq is the oriented curve given ik the figure - 3. Sa…

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Q: 5. Given a curve in the following parametric equation: x = 3- 2 sint, y = 4+ 2cos t, 0<ts Then: a.…

A:

Q: Let C denote the curve defined by the parametric equations I cost ly%3cost + t sint You are to find…

A:

Q: Consider the curve described parametrically by X = 3cos(t) , y = 3sin(t) , 0<t< 57/4 tch the curve,…

A: Given parametric Curve x= 3cos(t), y=3 sin(t), 0≤t≤5π4