Find an equation for the tangent plane to the graph of the function z = ex-y2 at

Question

Find an equation for the tangent plane to the graph of the function z = ex-y2 at the point (1,-1,1) (make sure you write both sides of the equation correctly, not just fill in one side, as was often the case in Webwork!) 1. on of the function f(x, y, z) = (3.029 + (1.97)2 + (5.99)2 x2 + y2 + Z2 at a suitable poi approximate Use a differential dz to approximate the change Az of the function z-x2 - xy + 3y2 when (x,y) changes from (3,1) to (2.96,-0.95). Compare the values of z and dz. 3. 4. Use differentials to estimate the amount of tin in a closed tin can with diameter 8cm and height 12cm if the tin is 0.04 cm thick

Explanation / Answer

1 . fx = 2x ex^2 -y^2 , fy =-2y ex^-y^2

At (1,-1,1)

fx=2 , fy=-2

Required equation of tangent

z-1=2(x-1)-2(y-1)

z= 2x -2y+1

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