Math Function Question

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Let f :R” + R be a Cl function. The graph of f is the surface M := {(x, f(x)) E R” x R | X E R”}
in R” x R.
(a) Let p:= (x0, f (xo)) E M. Find the space Tp.
(b) Show that Tp C TOM. That is show that any vector in the space To is a
space Tp is a tangent vector to M at p.
Note: you are not allowed to assume that Tp = TPM.

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graph

Space

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tangent vector

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