**Problem Statement: Find the Equation of the Tangent Plane** Given the equation of the surface: \[ Z^2 = e^{x^2y^2} + 7x + y^2 \] Find the equation of the tangent plane at the point \( P(1, 1, 3) \). This involves calculating the partial derivatives of the surface equation with respect to \( x \) and \( y \), evaluating them at the given point, and constructing the equation of the tangent plane using these derivatives. (Note: There are no graphs or diagrams to explain in detail.)

Q: Find the slope of the tangent line to the curve (a lemniscate) 2(x^2+y^2)2=25(x^2−y^2) at the point…

A: The given curve is:To find: The slope of the tangent line to the given curve at the point (-3,1).

Q: Why does the tangent function get undefined at some points? Please explain

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Q: (-2,1) 2x %3D 3. equation of the

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Q: 8x^2y^2 = (x^2 + y^2 )^3 List one point on the curve at which the tangent line is horizontal. Show…

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