Show that the set:
is not closed.
Let $a_n=-\frac{1}{n}+\frac{1+(-1)^n}{3}$ so that $S=\{a_n:n\in\mathbb N\}$. For odd $n=2k+1$ we have $a_{2k+1}=-\dfrac{1}{2k+1}$; for even $n=2k$ we _____ __________ _________ ____ __________ ____ ________ ___.
__________ ________ ________ ________ __________ ____ _______ __________ _____ ____ ______ ________.
_______ _______ _____ ________ _______.
___ ________ _________ _______ _________ ________.
____ _________ ___ _______ _________.
_________ _______ _____ ___ ____ __________ ______ ____ ___ ______ _________ _____.
______ _________ ______ __________ _______ _______ ___ ____ ________ _________ ______.
________ _______ ________ ______ ___ _________ ___ ___ _________.
___ __________ _______ _________ _______ ________.
_____ _______ __________ ______ ____ ____ ____ __________ ___.
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त्रिज्या जहाँ
की अभिसरण त्रिज्या ज्ञात कीजिए I
रीमान समाकलन से परिकलित कीजिए।
Find the supremum and infimum of the set:
Check whether f is uniformly continuous on [− ]1,1 or not.
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.
Find the value/s of x for which the series
is convergent.
Write the following statement, and its negation, using logical quantifiers. Also interpret its negation in words.
∃ x∈R such that x-1/3 > 0.