Calculate where is the curve $2² x² dy (x - 1)² + y² = 1 oriented counterclockwise.

Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: Find parametric equations for the tangent line of the curve r(t) = (3+ 3/7, to – 5t2 + 4, 3t³ + 2t²…

A: Find the parametric equations fot the tangent line

Q: Do the curves ri(t) = (t² + 3, t+1, t² – 5) and rž(s) = (4s, 2s – 2, s + 1) intersect? If so, at whi…

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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: nd the tangent plane to the equation z = a? – 4y? – 2y at the point ( – 3, 3, – 33)

A: In this question, concept of tangent  is used. Tangent A tangent is the line that runs parallel to…

Q: A curve is defined by the parametric equations x (t) = at² and d² y y (t) = bt where a and b are…

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Q: y = x3 + 2x2 – 5x + 4 of curve x = 2 : Find the equation for its tangent at the apsidal point. |

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Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: Sa(t) = t2 – 3 lu(t) = 2t +1' Consider the parametric curve -2 <t< 3. At which time(s) does the…

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Q: The slope of the tangent line to the graph of x + y + xy = 3 at (1, 1) is Blank 1. Blank 1 Add your…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1. Calculate y³ $ £ (-2² - sinz) dz + ( + v) ds. + dx dy, 3 3 where C is the circle of radius 1…

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Q: Find for the curve dx In (2x) + 5xy + y = 3.

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Q: Find the points on the curve z t? – 10t – 8, y = t² + 4t + 6 that have: A. a horizontal tangent line…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Find the equation of the tangent plane to the surface z = cos(6x) cos(3y) at the point (-2π/2,…

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Q: Find the tangent plane to the equation z = 5y cos(4x - 6y) at the point (6, 4, 20). z =

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Q: Suppose two dice (one red, one green) are rolled. Consider the following events: A: the red die…

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Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

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Q: Tangents are drawn to x² + y² = 1 from any arbitrary point P on the line 2x + y - 4 = 0. The…

A: Tangents are drawn to x2+y2=1 from any arbitrary point P on the line 2x+y−4=0. We have to find the…