Let C be the curve on the xy-plane that is the projection of a horizontal cross-section of the surface yz = In(x + 2) and that passes through the point (-1,0). Then the tangent line to C at (-1, 0) is represented by the equation x + y = 1.

Q: Find the equation of the tangent plane to the surface 2= 42 + 3y+7zy at the point (0,-1,3).

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Q: Find the point-slope equation of the tangent line to the parametric curve given by x = 1+ 2t° and y…

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Q: Find the equation of the tangent line to the curve of intersection of the surface z = x² - y² with…

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Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Find an equation of the tangent plane to the surface z = 3a + 3y + xy at the point (-1,-1,-5).

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Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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