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Section 14.1 : Tangent Planes and Linear Approximations

1. Find the equation of the tangent plane to \(\displaystyle z = {x^2}\cos \left( {\pi y} \right) - \frac{6}{{x{y^2}}}\) at \(\left( {2, - 1} \right)\). Solution
2. Find the equation of the tangent plane to \(z = x\sqrt {{x^2} + {y^2}} + {y^3}\) at \(\left( { - 4,3} \right)\). Solution
3. Find the linear approximation to \(z = 4{x^2} - y{{\bf{e}}^{2x + y}}\) at \(\left( { - 2,4} \right)\). Solution