Find a parametrization for the curve that matches the lower side of the parabola x-1=y2. A. x = t2+1, y = t², t< 0 %D B. x = t2 + 1, y = t, t < 0 C. x = t2+1, y = t, t> 0 D. x = t2-1, y = t, t< 0

Q: 3. cos Tx – x*y + e*z + yz = 4 at point Po(0, 1, 2). -

A: The given surface at the point P0 is    Cos(pix) - x2y +exz + yz = 4

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A: We will use the following method for finding the two required point.

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Q: Give the integral representing the length of the parametric curve x=t^3, y=t^4, 0≤t≤1.

A: Given: A parametric curve:   Now the length of the parametric curve is given by the formula:

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A: Area of ellipse initially  = Ai  = πab    Now, lengths of axis are changed,   They are  [ 2(1.0099)a…

Q: Consider the following. C: line segment from (0, 0) to (5, 10) (a) Find a parametrization of the…

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Q: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

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A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

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Q: Find an equation of the plane tangent to the following surface at the given points. z =6 cos (x- y)+…

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Q: Find the equation of the tangent plane to the surface 9x +36y +4z? = 108 at the point (-2,1,-3).…

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Q: Find a parametrization of the osculating circle for the parabola y= X sequar when x=1

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A: Given, r(t)=t i +(6t - t2)k ......(1) and z=x2+y2 .......(2)

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Q: In which of the choices below is a parametrization for the tangent line to the curve of intersection…

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Q: The curve a- y = e+ tanh y, a, y ER is given parametrically by Select one: O x(t) = t, y(t) = t + e'…

A: Parameterized the  curve which is given here

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Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A: First we have to find partial differentiation with respect to x , y and z of function f such that-

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A: given rθ=θ2,eθ,θ to find - cubic approximation at θ=0

Q: Let F(x, y) that starts at (0, 0)and ends at (1, 2). (6æ? + 4y) 7 + (4x + 3) j. Calculate la F . dř,…

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A: Finding the parameters:

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