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Math Help - Find the equations of the tangent plane and the normal line to the given surface

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    Find the equations of the tangent plane and the normal line to the given surface

    Find the equations of the tangent plane and the normal line to the given surface at the given point...

    z=e^xcos(y), (0,0,1)

    I just need a check of my work, I'm studying for my test, and this problem isn't in the back of the book to check.

    z_x=e^x|(0,0) =1
    z_y=-e^xsin(y)|(0,0) =0

    So plugging into the plane formula, I got
    z-1=1(x-0)+0(y-0)  z=x+1

    And the normal vector would be
    <1,0,-1> (this I'm unsure of)
    Thus giving parametric line equations of...
    x=t, y=0, z=1-t
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  2. #2
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    Quote Originally Posted by Rhode963 View Post
    Find the equations of the tangent plane and the normal line to the given surface at the given point...

    z=e^xcos(y), (0,0,1)

    I just need a check of my work, I'm studying for my test, and this problem isn't in the back of the book to check.

    z_x=e^x{\color{red}{\cos y}}|(0,0) =1
    z_y=-e^xsin(y)|(0,0) =0

    So plugging into the plane formula, I got
    z-1=1(x-0)+0(y-0)z =x+1

    {\color{red}{z-1=1(x-0)+0(y-0) =x}}

    And the normal vector would be
    <1,0,-1> (this I'm unsure of)
    Thus giving parametric line equations of...
    x=t, y=0, z=1-t
    A couple of typo's - in the above in red. The rest is OK.
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