What is estimate value?

Answer 1

An estimate is something when we cannot figure out a certain value EXACTLY, we took our best educated guess.

In terms of Algebra, it is the orthogonal projection of a vector (whatever that means)

In Calculus, it's the Linearization Lemma where we can approximate a function around x = a with the tangent passing through (a, f(a))

or

a Taylor polynomial approximate a function's behaviour (i.e. it's values"

or

an Upper bound or lower bound of a sequence/function to approximate its convergence/limit if it exist.