List questions from self-learning

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Prove that there exist a function $g(s,t)$ continuously dif on $B_r(s_0,t_0)$ s.t. $x_0=g(s_0,t_0)$ and $x^2+s^2+t^2=1$ for $x=g(s,t)$

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List Question

Some doubts regarding half range cosine series.

Am I understanding this integration right?

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Math Subjects that are prerequisites to Finite Element Method

Prove that there exist a function $g(s,t)$ continuously dif on $B_r(s_0,t_0)$ s.t. $x_0=g(s_0,t_0)$ and $x^2+s^2+t^2=1$ for $x=g(s,t)$

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