निम्नलिखित कथन तथा उनके निषेध को तर्कसंगत प्रमात्रकों का प्रयोग करते हुए आप किस प्रकार प्रस्तुत करेंगे? निषेध को शब्दों में भी दीजिए।
इस कथन का गणितीय रूप में है: \[ \exists x \in \mathbb{R}, \, \text{such that} \, x - \frac{1}{3} > 0 \] यह _______ _______ _______ _______ _________ ____ ___ ______ _____ ________.
_______ _______ _______ ____ ____ ____ ______ _____ _______ _____ ___ ____.
_________ ____ _______ ______ ______ __________ _____.
_____ _______ __________ _____ _____ ________ _________ __________ ___.
_____ ________ _________ ______ __________ ____.
_____ ____ _____ ______ ___ _______ _________ __________ ______.
________ ______ _______ _____ _______ _____ _______ ______ ___ _______ ________.
__________ ______ ___ ____ ______ ________.
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Apply the Cauchy’s integral test to evaluate:
Which of the following statements are true or false? Give reasons for your answers in the form of a short proof or counter-example, whichever is appropriate:
i) Every infinite set is an open set.
ii) The negation of p^~qis p→q.
iii) -1 is a limit point of the interval ]-2,1].
iv) The necessary condition for a function f to be integrable is that it is continuous.
The function f: R→R defined by f(x) = |x-2|+|3-x is differentiable at x = 5.
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रीमान समाकलन से परिकलित कीजिए।
A compact set.
A sequence which is divergent.
एक समुच्चय जिसका कोई सीमा बिन्दु नहीं है।