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L’Hopital’s Rule in the Integral Form
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UDC: 51 (071)
Publication Language: Russian
Stuc. intelekt. 2012; 17(3):411-419
Abstract: L’Hopital’s rule for an evaluation of indeterminate forms in the differential calculus can be represented in the integral form. In the result of such approach it is possible to formulate and prove an integral analogy of L’Hopital’s rule. This approach is allowed to proof the comparison test in the limiting form for improper integrals. Besides, the rule is applied to integrals with a variable upper limit. L’Hopital’s formula is suitable for a converging estimation of improper (first and second kinds) integrals and it allowed a possibility to formulate sufficient simple tests of converging and diverging of improper integrals.
Keywords: integral, convergence, divergence, L’Hopital’s rule, improper integral, uncertainty.
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