Surface level of a curve, does it influence the tangent plane?

jenuine
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Homework Statement



Does the surface level of a curve influence the tangent plane of that curve? If so, how do I find the tangent plane specific to that level?
 
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What do you mean, "surface level of a curve"?
 


Well for instance f(x,y,z)=xy+xz+xyz. Then the level surface f=10 would be xy+xz+xyz=10. I am just wondering whether this level surface will influence the equation of the tangent plane. If so, how do I find it with respect to that level surface.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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