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In this lesson, we will learn how to find the equation of a tangent plane to a suface at a given point.

Q1:

Find the equation of the tangent plane to the surface π₯ + π¦ = 4 2 2 at the point ο» β 3 , 1 , 0 ο .

Q2:

Find the equation of the tangent plane to the surface π₯ 4 + π¦ 9 + π§ 1 6 = 1 2 2 2 at the point οΏ 1 , 2 , 2 β 1 1 3 ο .

Q3:

Find the equation of the tangent plane to the surface π₯ + π¦ β π§ = 0 2 2 2 at the point ( 3 , 4 , 5 ) .

Q4:

Find the equation of the tangent plane to the surface π§ = π₯ π π¦ at the point ( 1 , 0 , 1 ) .

Q5:

Find the equation of the tangent plane to the surface π§ = π₯ + 2 π¦ at the point ( 2 , 1 , 4 ) .

Q6:

Find the equation of the tangent plane to the surface π§ = π₯ π¦ 2 at the point ( β 1 , 1 , 1 ) .

Q7:

Find the equation of the tangent plane to the surface π§ = β π₯ + π¦ 2 2 at the point ( 3 , 4 , 5 ) .

Q8:

Find the equation of the tangent plane to the surface π₯ + π¦ + π§ = 9 2 2 2 at the point ( 0 , 0 , 3 ) .

Q9:

Find the equation of the tangent plane to the surface π§ = π₯ π¦ at the point ( 1 , β 1 , β 1 ) .

Q10:

Find the equation of the tangent plane to the surface π§ = π₯ + π¦ 2 3 at the point ( 1 , 1 , 2 ) .

Q11:

True or False: If π΄ = π π π π₯ ( π , π ) and π΅ = π π π π¦ ( π , π ) are defined for a function π βΆ β β β ο¨ and a point ( π , π ) , then π΄ ( π₯ β π ) + π΅ ( π¦ β π ) = 0 defines the tangent line to the curve π ( π₯ , π¦ ) = 0 at ( π , π ) .

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