- #1
devinaxxx
Homework Statement
I tried to answer the following questions is about the curve surface [itex]z= f (x, y) = x^2 + y^2 [/itex] in the xyz space.
And the three questions related to each otherA.)
Find the tangent plane equation at the point [itex](a, b, a^2+ b^2) [/itex] in curved surface z .
The equation of the tangent plane at the point [itex](a, b, f (a, b)) [/itex] on z is given by the following equation[itex]Z-f(a,b)=f_x(a,b)(x-a)+f_y(a,b)(x-b)[/itex]So i got
[itex]
Z-(a^2+b^2)=2a(x-a)+2b(x-b)[/itex]
[itex]2ax+2by-(a^2+b^2)[/itex]2)
when the tangent plane of the previous question moves pass through the point (0,0,-1). Find The equation for a plane S that contains the contact trajectory.Tried to put 0,0,-1 to equation in number 1
[itex]-1=-(a^2+b^2)[/itex]
[itex]z=1 [/itex] is S(?) But i wasnt so sure what is S plane here and what is the relation with Z?
3.
Calculate the volume V of the part surrounded by [itex]z=x^2+y^2 [/itex] and the plane S
Note :
I was confuse about number 3, what is the area surrounded by S and Z (?)
Since i wasnt so sure about graph of S and Z here
can you help me to picture s and z? and also give me hint about the integration of the volume?
Homework Equations
The Attempt at a Solution
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