Indeed, it is needed to prove both the mean value theorem and the existence of Taylor series.
12.
These refinements of Taylor's theorem are usually proved using the mean value theorem, whence the name.
13.
Given that, the fundamental theorem of the calculus and the mean value theorem imply that f is everywhere 1.
14.
That the latter is a Hilbert space at all is a consequence of the mean value theorem for harmonic functions.
15.
The main conjecture of Vinogradov's mean value theorem is that the upper bound is close to this lower bound.
16.
Each rectangle, by virtue of the mean value theorem, describes an approximation of the curve section it is drawn over.
17.
The mean value theorem is the special case of Cauchy's mean value theorem when " t " } }.
18.
The mean value theorem is the special case of Cauchy's mean value theorem when " t " } }.
19.
The mean value theorem in one variable tells us that there exists some " t * " between 0 and 1 such that
20.
His work contains mathematical objects equivalent or approximately equivalent to infinitesimals, derivatives, the mean value theorem and the derivative of the sine function.
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