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Find an equation of the tangent plane to the given surface at the specified point.z=e^(x^2 + y^2) (1, −1, 1)

Question

Find an equation of the tangent plane to the given surface at the specified point.

z=e^(x^2 + y^2)

 
(1, −1, 1)
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Step 1

Given equation of the surface is,

z=e
.(1)
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z=e .(1)

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Step 2

And the given points is (1,-1,1).

Partially differentiate the equation of the surface with respect to x and y,

= e(2x)
'(2y)
(2)
Zx
.(3)
Z
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= e(2x) '(2y) (2) Zx .(3) Z

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Step 3

Equation of the tangent plan...

2-2, (x-)z, (X0. Yo) +(y-y)z, (4,)
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2-2, (x-)z, (X0. Yo) +(y-y)z, (4,)

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