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Nov
20
awarded  Student
Nov
14
comment Prove continuity of a simple polynomial
@sillyme, the definition of continuity in terms of sequences says that $\forall\ x_k \rightarrow A$ you must have $f(x_k) \rightarrow f(A)$. Your goal is to prove the reverse. Hence, $\forall$ turns into $\exists$. In other words, you need only one sample to present that does not deliver equal limits. The concrete choice in my case is just a matter of convenience - we need some simple sequence that tends to the point in question. Does this answer your question?
Nov
14
revised Correct terminology for polylines, their segments, knots, etc.
added 20 characters in body
Nov
14
comment Correct terminology for polylines, their segments, knots, etc.
@HandeBruijn Thanks a lot! Not exactly numerical methods, but pure approximation theory, but it doesn't seem to make a difference.
Nov
14
awarded  Editor
Nov
14
revised Correct terminology for polylines, their segments, knots, etc.
more background information
Nov
14
asked Correct terminology for polylines, their segments, knots, etc.
Nov
14
answered Prove continuity of a simple polynomial
Apr
16
awarded  Supporter
Nov
23
comment Partial derivative notation: $\left.\frac{\partial \cdot}{\partial\cdot} \right|_{u=T}$
The short answer is: because $T$ is the function argument, that is, considered constant in the RHS; but you can only differentiate w.r.t. independent variable. For example, put you want $f(t,5)$. The RHS becomes meaningless.
Nov
22
awarded  Teacher
Nov
22
answered Partial derivative notation: $\left.\frac{\partial \cdot}{\partial\cdot} \right|_{u=T}$