## Related questions with answers

Question

Answer each question about the surface area S on a surface given by a positive function z = f(x, y) over a region R in the xy-plane. Explain each answer. (a) Is it possible for S to equal the area of R?

Solution

VerifiedAnswered 11 months ago

Answered 11 months ago

Step 1

1 of 2Consider function $z=f(x,y)=1.$ Then it implies that

$f_x=f_y=0.$

Therefore, the following holds

$S=\int\int_R\sqrt{1+f_x^2+f_y^2}\>dydx=\int\int_R\>dydx=A_R.$

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