2. Consider the parametric equation r(t) = (1 – t°, t(1 – t)) where –1

Q: Construct the inverse matrix (if it exists) for the following matrices: [12 61 (а) А %— 4 2. 1 -2]…

A: We will find out the required solution.

Q: 8. For the curve given by r(t)=√√² +8 i + In(t² + 8)j + tk 2 find: a. r'(t)

A: Introduction: For a vector curve rt=ati+btj+ctk, the tangent line at the point of contact t=t0 is…

Q: (c) Find dy/dx at t = T/3. (d) Include in sketch for (a) the tangent line to the curve at t = T/3…

A: We have to find the equation of tangent line.

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: x = 7 te', y = (t + 1)e', 0stsi Set up an integral that represents the area of the surface obtained…

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Q: 2. Consider the parametric curve r = t + 1, y = t - t. dy (a) Find d.r dy (b) Find da?

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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 parametric curve x = 3t5 + 1, y = 10t³ – 1, t e R. a) Find the values of t where the…

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Q: Find the slope and concavity of the parametric curve at the point t = (1/2), x(t) = (1/2)t² -1,…

A: To find the slope of the curve at t = 1/2, we need to find the derivative of y with respect to x:…

Q: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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Q: Sketch the parametric curve at R* whose parameterization is given by a (t) = (cos (t), sin (1), t),…

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Q: Find the length of the curve defined by the parametric equations t, y = 5 In((t/6)? – 1) I = from t…

A: Given, x = 56t , y = 5lnt62-1 = 5lnt2-36-5ln(36)and 7≤t≤10

Q: a) A curve has equation e3x. i) Find dx — e2x e3ye-2y = 3 in terms of x and y. ii) Find the equation…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Sketch the curve given by the parametric equations x= t³ - 1 and y= t² + t. Construct a table with…

A: Given problem:- Sketch the curve given by the parametric equations x= t3 - 1 and y= t2 + t.…

Q: Find the length of the parametric curve: x = 2t + 1; y = t? – 3,0 <t < 5

A: Given that: x=2t+1,  y=t2-3,0≤t≤5To  calculate   dxdt  and   dydt,dxdt=ddt2t+1=2dydt=ddtt2-3=2t

Q: iez3 dz. ty z – i

A: In this question, we need to find the value of complex integral. Here first we find the contour and…

Q: Fill in the template. We want the 3D TANGENT line to the associated parametric curve: r (t) = (tan-…

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Q: 4. Consider the parametric curve x = cost, y = sin cost, te [-T, π]. (a) Show that (0,0) is a point…

A: Consider the parametric curve given by  and , where  belongs to .a) To show that  is a point of…

Q: The parametric equations of a curve is x = 3 sin t, y=3 cos t and z = 4. (a) Sketch the curve r(t)…

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Q: dy for the parametric curve x= 2e', y= sin(1 + e' ) dx Find

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