Find an equation of the plane tangent to the following surfaces at the given poi

tabita57i

tabita57i

Answered question

2021-09-17

Find an equation of the plane tangent to the following surfaces at the given point. z=tan1xy;(1,1,π4)

Answer & Explanation

Benedict

Benedict

Skilled2021-09-18Added 108 answers

We know that equation of tangent plane on the surface z=f(x,y) at the point (a,b, f(a,b)) is
z=fx(a,b)(xa)+fy(a,b)(yb)+f(a,b)
The function is z=tan1(xy)
Let's find fx and fy
fx(x,y)=(tan1(xy))x=yx2y2+1
fy(x,y)=(tan1(xy))y=xx2y2+1
At point (1,1,π4) the values of derivatives are
fx(1,1,π4)=12
fy(1,1,π4)=12
Therefore, the equation of tangent plane at the point (1,1,π4) is
z=12(x1)+12(y1)+π4
z=12x+12y+π41
Results:
z=12x+12y+π41

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