A Course of Mathematical Analysis, Volume 1 |
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absolutely convergent antiderivative arbitrary bounded called Cauchy's Cauchy's criterion closed interval complex number continuous function continuously differentiable coordinates corresponding curve decimal definite integral denote different from zero divergent elementary functions elements equal to zero equation Example exists expression finite number follows fraction function defined function f given graph Hence holds implies improper integral increment infinite inverse function lemma Let us consider lim f(x limit lim limit point natural number neighbourhood nondecreasing nonnegative obtain obviously open interval open set parameter partial derivatives plane point belonging point xº polynomial positive number Proof properties proved R₁ rational numbers real numbers respectively right-hand side satisfying the inequality sequence sufficiently small suppose supremum tangent Taylor's formula tends to zero theorem tion uniformly convergent values vector whence ди ду дх