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

Falak Kinney

Falak Kinney

Answered question

2021-10-31

Find an equation of the tangent plane to the given surface at the specified point.
z=(x+2)22(y1)25,(2,3,3)

Answer & Explanation

BleabyinfibiaG

BleabyinfibiaG

Skilled2021-11-01Added 118 answers

Equation for tangent plane at (x0,y0,z0) is given by
zz0=fx(x0,y0)(xx0)+fy(x0,y0)(yy0)
Given that
f(x,y)=(x+2)22(y1)25
Therefore
fx=2(x+2)
fx(2,3)=2(2+2)=8
fy=4(y1)
fy(2,3)=4(31)=8
Equation of the plane at (2,3,3) is
z3=fx(2,3)(x2)+fy(2,3)(y3)
Substitute
fx(2,3)=8,fy(2,3)=8
z3=8(x2)8(y3)
z3=8x168y+24
z=8x8y+11
Result z=8x8y+11

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?