Find the equation of the tangent plane and the normal line to the given surface at the specified point.20zay9ysinz) = 2048Point: (2, 4, 0)(a) Equation of tangent plane.Be sure to enter an equation.(b) Equation of normal lineYou will need to express your answer with symmetric equations but in two parts.(i) Symmetric equations withand y(ii) Symmetric equations with æ and z

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Asked Nov 5, 2019
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Find the equation of the tangent plane and the normal line to the given surface at the specified point.
20z
ay9ysinz) = 2048
Point: (2, 4, 0)
(a) Equation of tangent plane.
Be sure to enter an equation.
(b) Equation of normal line
You will need to express your answer with symmetric equations but in two parts.
(i) Symmetric equations with
and y
(ii) Symmetric equations with æ and z
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Find the equation of the tangent plane and the normal line to the given surface at the specified point. 20z ay9ysinz) = 2048 Point: (2, 4, 0) (a) Equation of tangent plane. Be sure to enter an equation. (b) Equation of normal line You will need to express your answer with symmetric equations but in two parts. (i) Symmetric equations with and y (ii) Symmetric equations with æ and z

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Expert Answer

Step 1

Given: -

20z
- xy4 +9ysinz2048
x
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20z - xy4 +9ysinz2048 x

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Step 2

To find: -

a) Equation of tangent plane
b) Equation of normal line
symmetric equation with x and y
i symmetric equation with x and :
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a) Equation of tangent plane b) Equation of normal line symmetric equation with x and y i symmetric equation with x and :

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Step 3

Calculation: -

Pa...

To find gradient, using formula
of
(x, y, z),
(x, y,z)>
(x,y,z),
gradf
=<fr(xe, y),f (x.,y.),f(x., y.
Lo
Now, finding the gradient,
20
9y cos z >
-20z
+3x2y4,4x'y +9sin z,
gradf
2, y. = 4, z. 0, to find the gradient at
Now, putting the values of x.
that point
20(0)
+3(2) (4)',4(2) (4)* +9sin(0)-2)
(2)
20
+9(4)cos(0)>
gradf
=3072,2048,46>
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To find gradient, using formula of (x, y, z), (x, y,z)> (x,y,z), gradf =<fr(xe, y),f (x.,y.),f(x., y. Lo Now, finding the gradient, 20 9y cos z > -20z +3x2y4,4x'y +9sin z, gradf 2, y. = 4, z. 0, to find the gradient at Now, putting the values of x. that point 20(0) +3(2) (4)',4(2) (4)* +9sin(0)-2) (2) 20 +9(4)cos(0)> gradf =3072,2048,46>

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Math

Calculus

Derivative