9.4: Tangent Planes and Linear Approximations
- Page ID
- 144344
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- Find a vector tangent to the curve \(x^2 + xy + y^2 = 3\) at point \(P(-1, -1)\).
- Find a vector tangent to the curve \((x^2 + y^2)^2 = 9(x^2 - y^2)\) at point \(P(\sqrt{2}, 1)\).
- Find a vector tangent to the curve \(2x^3 - x^2y^2 = 3x - y - 7\) at point \(P(1, -2)\).
- Find the equation for the plane tangent to the surface \(-8x - 3y - 7z = -19\) at \(P(1, -1, 2)\).
- Find the equation for the plane tangent to the surface \(z = -9x^2 - 3y^2\) at \(P(2, 1, -39)\).
- Find the equation for the plane tangent to the surface \(x^2 + 10xyz + y^2 + 8z^2 = 0\) at \(P(-1, -1, -1)\).
- Find the equation for the plane tangent to the surface \(z = \ln(10x^2 + 2y^2 + 1)\) at \(P(0, 0, 0)\).
- Find the equation for the plane tangent to the surface \(z = e^{7x^2 + 4y^2}\) at \(P(0, 0, 1)\).
- Find the equation for the plane tangent to the surface \(xy + yz + zx = 11\) at \(P(1, 2, 3)\).
- Find the equation for the plane tangent to the surface \(z = \sin x + \sin y + \sin(x + y)\) at \(P(0, 0, 0)\).
- Find the equation for the plane tangent to the surface \(x^2 + y^2 + z^2 = 1\) at \(P\left(\dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}, 0\right)\).