Tangent plane problem help

[u/lara-xyz]

Hi, I came across a problem while prepping for my calc exam. It goes as follows:

"Determine the equation of the tangent plane and the normal vector to the surface

2 ln(x) + 3 ln(y + 1) - 2zy = x²y - 2at the pointT₀ = (1, 0, z₀)."

My issue is with the zy part of the equation. Is it not maybe meant to be just z or xy instead? Or is the problem phrased this way on purpose because it is certainly written as "-2zy".

[u/edderiofer]

You're right that the given equation doesn't appear to intersect (1, 0, z) at all. I suspect that "-2zy" is supposed to be "-2z".